MTS / POSTMAN / GDS TO PA/ PA RECRUITMENT MATERIAL

PROFIT & LOSS :                                                                                  To download full  Chapter,  click below link http://www.viewdocsonline.com/document/pd4zbn

1. Profit = Selling Price - Cost price

2. Selling Price = Cost Price + Profit

3. Cost Price = Selling Price - Profit

4. Loss = Cost Price - Selling Price

5. Selling Price = Cost Price - Loss

6. Cost price = Selling Price + Loss

Gain% = (Gain/C.P)*100

Loss% = (Loss/C.P)*100

7. Percentage profit / loss is always calculated on CP unless otherwise stated.

8. Profit Percentage = (Profit x 100) / CP

9. Loss Percentage = (Loss x CP) / CP

10. Selling Price = {[(100+ Gain %) x CP] / 100}

11. Selling Price = {[100- Loss %) x CP] /100}

12. Cost Price = {(100 x SP) / (100+ Gain %)}

13. Cost Price = {(100 x SP) / (100 - Loss %)}

14. If a man buys 'p' articles for 'a' rupees and sells 'q' articles for 'b' rupees. Then,

The % profit or loss = (p x b) - (q x a) / (a x q).

Note: If the Sign is +ve, there is gain. If the sign is -ve, there is a loss.

Eg : A trader buys oranges at 9 for Rs. 16 and sells them at 11 for Rs. 20. What does he gain or lose percent?

Ans: % profit or loss = [(9 x 20) - (16 x 11)]/ 16 x 11

= 2 3/11 %.

Since the sign is +ve, there is a gain of 2 3/11%.

15. If a shopkeeper sells his goods at x% loss on cost price but uses y gm instead of z gm, then,

His % profit or loss = [(100 - x) (z/y)] - 100.

Eg: A dishonest trader sells goods at 6 ¼ % loss on cost price but uses 875 gm instead of 1 kg. What is his percentage profit or loss?

Ans: Profit or loss percentage = [(100-6 ¼) (1000/875)] - 100

= [(375/4) (8/7)] - 100

= (107.1428) -100

= 7.1428 %

Since sign is +ve, there is a profit of 7.1428%.

16. If a shopkeeper sells his goods at x% profit on cost price but uses y gm instead of z gm, then,

His % profit or loss = [(100 + x) (z/y)] - 100.

Eg: A dishonest trader sells goods at 4 % gain on cost price but uses 840 gm instead of 1 kg. What is his percentage profit or loss?

Ans: Profit or loss percentage = [(100+4) (1000/840)] - 100

= [123.8095] - 100

= 23.8095%

Since sign is +ve, there is a profit of 7.1428%.

17. When two articles are sold at the same price such that there is a Profit of x % on one article and a Loss of x% on the other. Then Percentage Loss is:

= (Common profit or loss) 2 /100

= X2 /100

18. Marked Price or List Price is the price that is indicated or marked on the product or it is the price, which is given in the price list. This is the price at which the product is intended to be sold. However, there can be some DISCOUNT given on this price and consequently, the actual Selling Price of the product may be less than the Marked Price.

Selling Price = Marked Price - Discount.

19. Discount Percent = (Marked Price - Selling Price) x 100 / Marked Price

20. If the successive discounts given on a product are p%, q% and r%, then the selling price after all the discounts is:

= [Marked Price x (100-p) (100-q) (100-r)]/ 100 x 100 x 100

21. If 'x' articles are purchased for 'p' rupees and 'y' articles are sold for 'p' rupees. Then, Percentage profit / loss = (x-y) / y.

22. If selling price of 'x' pens is equal to the cost price of 'y' pens. Then profit percentage = (y-x) x 100 / x

E.g 2: The selling price of 12 pens is equal to the cost price of 20 pens. Find the profit percentage?

Ans: Percentage profit = (20 - 12) / 20

= 8/20

= 66.66%.

E.g3: If 12 oranges are purchased for Rs. 100 and 10 oranges are sold for Rs. 100. Find the percentage profit / loss ?

Ans: Percentage Profit = [(12 - 10) /10]x 100.

= (2 /10) x 100

= 20 %.

23. By using false weight, if a substance is sold at cost price the overall gain % is given by [(100 + Gain %) / 100]. = True weight/ False weight.

24.      By selling an article for Rs. X, a man loses l%. At what price should he sell it to gain y%?       (or)

A man lost l% by selling an article for Rs. X. What percent shall he gain or lose by selling it for Rs. Y?

(100 – loss%) : 1^st S.P. = (100 + gain%) : 2^nd S.P.

2.      A man sold two articles for Rs. X each. On one he gains y% while on the other he loses y%. How much does he gain or lose in the whole transaction?

In such a question, there is always a lose. The selling price is immaterial.

Formula for loss %

3.      A discount dealer professes to sell his goods at cost price but uses a weight of 960 gms. For a kg weight. Find his gain percent.

 

Formula: Gain % =

12.C.P = S.P/(1-losspart)

13.C.P=S.P*[100/(100+g1)]*[100/(100+g2)]*[100/(100+g3]

14.S.P=C.P*[(100+g1)/100]*[(100+g2)/100]*[(100+g3)/100]


15.C.P = [(S.P1-S.P2)/x2-x1]*100


x1 ---------> gain1 (or) loss1

x2 ---------> gain2 (or) loss2

16.S.P=C.P + [(C.P*g)/100]

17.Overall gain or loss =(x1*g1)-(x2*L1)+(x3*g3)


Where x1,x2,x3 ----------> Parts of items sold

1.     When a Person sells two similar items, one at a gain of x% and the other at a loss of x%, then the seller always incurs a loss of is :

Loss % = {(Common Loss and Gain %) / 10} ² = (x/10)²

2.     When a Person buys two similar items, sells one at a gain of x% and the other at a loss of x%, then the seller incurs no gain no loss

3.     If a trader profess to sell his goods at cost Price, But uses false weights, then

Gain % = {(error)/ ((True Value)-(Error))}*100 %

 Important Points to remember that:

§  Profit % and Loss % is fully based on Cost Price alone.

Profit =10% i.e. 10% of Cost Price is Profit .This is the meaning of 10% Profit.

§  Discount is fully based on the Market Price/Retail Price/List Price.

Discount = 10% i.e. 10% on Market Price is Discount .This is the meaning of 10% Discount.

§  Doubling the price and then reducing it by 50% does not yield 50% profit – the net effect is no-profit-no-loss.

§  Successive discounts of 10%, 20% and 30% does not yield an overall 60% discount –the actual total is only 49.6%.

§  Successive discounts of 25%, 10% and 5% is not the same as successive discounts of 20%, 15% and 5% although both add up to 40%. The actual total discounts are 35.875% and 35.4% respectively.

§  A is 200% of B => A = 2B. But A is 200% more of B = >A = 3B. Similarly, P is twice as old as Q => P’s age = 2 × Q’s age, but A is twice older than B = >A’s age = 3 × B’s age.

Example:

1.A man buys an article for Rs.27.50 and sells it for Rs.28.60.Find his gain percent ?

Buys denotes the cost price , c.p = 27.50

Sells denotes the selling price, s.p = 28.60

For finding the profit % by two methods.

1.     find the profit and apply on (3) profit % formula

2.     Directly apply in 7 th formula.

Decide which is easy for you .

First method

Profit = 28.60 – 27.50 = 1.10

Profit % = (1.10 / 27.50)*100 = 4%

Second Method

60. = ((100 + gain% )/100 }27.50

(28.60*100 )/27.50 = 100 + gain %

Gain % = 104-100 = 4%

2. John bought a satellite radio for rs 4,000 and sold it at a loss of 5% due to unavoidable circumstances. Find his Selling Price ?

Cost Price = 4000

Loss = 5 %

From the formula 7 ,we can get it directly ,

Selling Price = rs3800.

Check with your answer 

3.If the cost Price of two articles is 1000 each, one of them is sold at 10% profit and the other at 10% loss. Find the percentage of profit or loss on the whole transaction ?

From formula 12 ,we can say directly No Loss No Gain .Lets Check out,

Total Cost Price = Rs.2000.

Need to find the total Selling Price ,

By the Formula 7,

Selling Price of one article (10% profit) = 1100

By the Formula 8,

Selling Price of another article (10% loss) = 900

So the total selling price = 1100+900 = Rs.2000.

Selling Price = Cost Price .So No Loss No Gain in whole transaction.

 4.If the Selling Price of two articles is 1000 each, sold one at 10% profit and the other at 10% loss. Find the percentage of profit or loss on the whole transaction ?

From formula 11, we can say that loss % = (10/10)²= 1%

Lets check out in another way ,

Total Selling Price = Rs.2000

By the Formula 7,

Cost Price of one article (sold at 10% profit) = 909.09

By the Formula 8,

Cost Price of another article (sold at 10% loss) = 1111.11

Total Cost Price = 909.09+1111.11 = Rs.2020.20

here C.P > S.P . So loss incurs in whole transaction.

Loss % = {(2020.20 – 2000 )/ 2020.20 }*100 = 1.00%

We have verified the answer in both the way. So we can use formula directly 

5. The selling price of 15 chairs is equals to the cost price of 20 chairs. Find the Profit or Loss % ?

Given, S.P of 15 chairs = C.P of 20 chairs.

From the above eqn we can conclude that we can get profit. Because Selling 15 chair itself we will get the total cost of the 20 chairs. So we get the profit of selling 5 chairs.

First method,

Using Profit% formula we can find the answer,

Profit% = (Profit/ Cost Price )*100

Profit % = {(S.P of 5 chairs)/(S.P of 15 chairs or C.P of 20 chairs) }*100

Profit % = (5/15)* 100 = 33.33%

Second method,

Let we take cost price be Rs 1,selling price be Rs x.

from the eqn, we can write 15x = 20 ; x = Rs. 1.3333

S.P > C.P , So we will get profit only. Profit = 1.3333 – 1.00 = Rs. 0.3333

Profit % = (0.3333/1 )*100 =33.33%

Third method,

Let we take cost price be ‘rs x’ and selling price be ‘rs y’. We can do this way also. Try this method

Examples

1. If a man buys a pen for Rs.25 and sells it for Rs.30, then he makes a Profit of 30 – 25 = Rs.5.

2. If a man buys a pen for Rs.25 and sells it for Rs.20, then he makes a Loss of 25 – 20 = Rs.5.

3. A man buys a pen for Rs.25 and sells it for Rs.30, then his gain% = 

4. A man buys a pen for Rs.25 and sells it for Rs.20, then loss% = 

5. A fruit seller purchases oranges at the rate of 3 for Rs 5 and selIs them at 2 for Rs 4. His profit in the transaction is

Sol: Let number of iranges = LCM of 2,3,4,5 = 60 

cost price of 60 oranges = (5/3 * 60) = 100
sell price of 60 oranges = (4/2 * 60) = 120
profit % = 20%

6. There would be 10% loss if a toy is sold at Rs 10.80 per piece. At what price should it be sold to earn a profit of 20%

Sol: 90:10.80 = 120:x or 90/10.80 = 120/x
x = (120 * 10.80)/90 = 14.4 hence SP = 14.4

7. A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 21 per kg, then his gain percent is

Sol: Suppose he bought 5 kg and 3 kg of tea.
Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150.
Sell price = Rs. (8 x 21) = Rs. 168.
profit % = (18/150) * 100 = 12%

8. A person bought 20 liters of milk at the rate of Rs 8 per liter. He got it churned after spending Rs 10 and got 5 kg of cream and 20 liters of toned milk. If he sold the cream at Rs. 30 per kg and toned milk at Rs 4 per liter, his profit in the transaction

Sol: Investment Rs. (20*8 + 10) = Rs. 170.
Receipt = Rs. (30*5 + 20*4) = Rs. 230.
profit %=[(60/170) * 100] % = 35.29% = 35.3%.

9. A dealer sold two of his cattle for Rs. 500 each. On one of them he lost 10% on the other, he gained 10%. His gain or loss percent in the entire transaction was

Loss%= (common gain or loss % / 10)² = (10/10)² % = 1%.

If the cost price of 12 tables is equal to the selling price of 16 tables, the loss percent

Cost price of 1 table = 1
cost price of 16 table = 16
sell price 16 table = 12
Loss = (4/16)*100 = 25%

10. A shopkeeper sold an article for Rs 2564.36. Approximately what was his profit percent if the cost price of the article was Rs 2400

Sol: Gain % = (164.36*100/2400) = 6.84% = 7% approx

11.Vilcas bought paper sheets for Rs 7200 and spent Rs 200 on transport. Paying Rs 600, he had 330 boxes made, which he sold at Rs 28 each. His profit percentage is :

Sol: Total investment = Rs. (7200+200+ 600) Rs. 8000.
Total receipt Rs. (330 x 28) = Rs. 9240.
profit % = [1240/8000] * 100 = 15.5

12. By selling 45 lemons for Rs 40, a man loses 20 %. How many should he sell for Rs 24 to gain. 20 % in the transaction?

Let S.P. of 45 lemons is Rs. x.
80 : 40 = 120 : x or 80/40 = 120/x or x = 40 * 120 / 80 = 60
lemons sold For Rs. 60, = 45
lemons sold For Rs. 24, = (45/60) * 24= 18.

13. If books bought at prices ranging from Rs 200 to Rs 350 are sold at prices ranging from Rs 300 to Rs 425, what is the greatest possible profit that might be made in selling eight books.

Sol: Let cost price = 200*8 = 1600
greatest price = 425 * 8 = 3400
profit required 3400- 1600 = 1800

14. A man bought a number of oranges at 3 for a rupee and an equal number at 2 for a rupee. At what price per dozen should he sell them to make a profit of 20 %

Sol: let us assume he bought 12 oranges of each kind CP of 2 dozen(12*2) = ((1/3) *12) + (1/2) * 12) = 10
profit = 20%
sp of 2 dozen = 120% of 10 = 12
sp per dozen = 6

15. when a commodity is sold for Rs 34.80, there is a loss of 25%. What is the cost price of the commodity?.

Sol: sell price = 34.80 loss = 25%
cost price = (100*34.80 / 75) = 46.40

16. By mixing two qualities of pulses in the ratio 2: 3 and selling the mixture at the rate of Rs 22 per kilogram, a shopkeeper makes a profit of 10 %. If the cost of the smaller quantity be Rs 14 per kg, the cost per kg of the larger quantity is:

Sol: Cost Price of 5 kg = Rs.(14*2 + x*3) = (28 + 3x).
Sell price of 5 kg = Rs. (22x5) = Rs. 110.
(110 - (28 + 3x)/(28 + 3x)) * 100 = 82-3x/28 + 3x = 1 / 10
820 - 30x = 28 +3x ; 33x = 792 ; x = 24

17.A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. He sell  the radio for Rs 300. The profit percent of the retailer is:.

Sol; cost price = (225 + 15) = 240 sell price = 300
gain = (60/240)*100 = 25%

18.A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 1 less, he would have made a profit of 10%. The C.P. of the article was:.

Sol: let original cost price is x its cost price = 105/100 * x = 21x/20
New Cost price = 95/100 * x = 19x/20 new Sell price = 110/100 * 19x/20 = 209x/200
[(21x/20) - (209x/200)] = 1 or x = 200

19.A horse and a cow were sold for Rs. 12000 each. The horse was sold at a loss ot 20% and the cow nt gain ot 20% 1 he entire transaction resulted in.

Sol: Total S.P. Rs, 24000.
C.P. of horse =Rs. [(100/80) x 12000] = 15000.
C.P. of cow = Rs.[(100/120) x 12000] = 10000
Total C.P. = Rs. 25000.
profit = Rs. (25000—24000) Rs 1000.

20.A man buys oranges at Rs 5 a dozen and an equal number at Rs 4 a dozen. He sells them at Rs 5.50 a dozen and makes a profit of Rs 50. How many oranges does he buy

Sol : Cost Price of 2 dozen oranges Rs. (5 + 4) = Rs. 9.
Sell price of 2 dozen oranges = Rs. 11.
If profit is Rs 2, oranges bought = 2 dozen.
If profit is Rs. 50, oranges bought = (2/2) * 50 dozens = 50 doze

21.A shopkeeper bought an article for Rs 319.60. Approximately, at what price should he sell the article to make 25% profit?

Sol: sell price = 125% of 319.60 = (125/100) * 319.60 = 399.50 = 400 Rs

22. Bhajan Singh purchased 120 reams of paper at Rs 80 per ream. He spent Rs 280 on transportation, paid octroi at the rate of 40 paisa per ream and paid Rs 72 to the coolie. If he wants to have a gain of 8 %, what must be the selling price per ream?

Sol: Total investment = Rs. (120 * 80 + 280 + (40/100) * 120 + 72).
= Rs. (9600 + 280+48 + 72) = Rs, 10000.
Sell price of 120 reams = 108% of Rs. 10000 = Rs. 10800.
Sell Price per ream = Rs. [10800/120] = Rs. 90.

23.A sells a bicycle to B at a profit of 20 % and B sells it to C at a profit of 25 %. If C pays Rs 1500, what did A pay for it ?.

Sol: 125% of 120% of A = 1500
[(125/100) * (120/100)*A]= 1500.
A=[1500*(2/3)]= 1000.

24.A man sold 250 chairs and had a gain equal to selling price of 50 chairs. His profit percent is

Sol: sell price of 200 chairs = cost price of 250 chairs
let cost price of each chair is Rs 1
cost price of 200 chairs = 200
sell price of 200 chairs = 250
gain % = (50/200*100) = 25%
(since; gain = sp of 250 chairs - cost price of 250chairs hence sp of 250 chairs - cost price of 250 chairs = SP of 50 chairs)

25. Ajay bought 15 kg of dal at the rate of Rs 14.50 per kg and 10 kg at the rate of Rs 13 per kg. He mixed the two and sold the mixture at the rate of Rs 15 per kg. What was his total gain in this transaction?

Sol: Cost price of 25 kg = Rs. (15 x 14.50 + lOx 13) = Rs. 347.50.
Sell price of 25 kg = Rs. (25 x 15) = Rs. 375.
profit = Rs. (375 — 347.50) = Rs. 27.50.

26. Raghu bought 4 dozen oranges at Rs 12 per dozen and 2 dozen oranges at Rs 16 per dozen. He sold them all to earn 20% profit. At what price per dozen did he sell the oranges?.

Sol: Total CP = (12*4 + 16 *2) = 80
SP of 6 dozen oranges = [(120/100 )* 80)] = 96
sell price per dozen =16

27.Two mixers and one T.V. cost Rs. 7000, while two T.V.s and a mixer cost Rs, 9800. The value of one T.V. is:.

Sol: Let C.P. of a mixer be Rs. x and that of a T,V. be Rs. y.
Then, 2x + y = 7000 and 2y + x = 9800.
Multiplying 2nd equatien by 2 and subtracting first from it, we get
3y = 19600 - 7000 = 12600 or y = 4200 C.P. of a T.V. = Rs. 4200

28.Rahim buys mangoes at the rate of 3 kg for Rs 21 and sells them at 5 kg for Rs 50. To earn Rs 102 as profit, he must sell

Sol: rate of buying = 7; rate of selling = 10 to gain 3 Rs he must buy 1 kg
for 102 profit he must buy = (102/3) = 34

29.If the manufacturer gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then the cost of production of a table, the retail price of which is Rs 1265 was

Sol: 125 % of 115% of 110% ofP= 1265.
[(125/100)*(115/100)*(110/100)]P = 1265 hence (253/160)p= 1265
P = (1265 * 160)/253 = 800

30.A man sells two houses at the rate of Rs. 1.995 lakh each. On one he gains 5% and on the other, he loses 5%. His gain or loss percent in the whole transaction Is :.

Sol: Loss%= (common gain or loss % / 10)² = (5/10)² % = 0.25%.

31. An article when sold at a gain of 5% yields Rs 15 more than when sold at a loss of 5%. What is the C.P..

Let the CP is x then [(105x/100 ) - (95x/100)] = 15 or x = 150

32. If by selling 110 mangoes, the C.P. of 120 mangoes is realised, the gain percentage is 

Sol:

Let C.P. of each mango be Re. 1.

C.P. of 110 mangoes = Rs. 110; S.P. of 110 mangoes = Rs. 120.

Gain% = 10 110  x 100 % = 9 1 11

33. The ratio of the cost price and the selling price is 4 : 5. The profit percent is : Sol:

Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x. Gain = Rs. (5x - 4x) = Rs. x.

Gain% = x 4x  x 100 % = 25%.

34. A man buys an article for 10% less than its value and sells it for 10% more than its value. His gain or loss percent is :

Sol: Let the article be worth Rs. x.

C.P. = 90% of Rs. x. = Rs. 9x 10 ; S.P. = 110% of Rs, x = Rs. 11x 10

Gain = Rs. 11x 10 - 9x 10  = Rs. x 5

Gain% = x 5 x 10 9x  x 100 % = 22 2 9 % > 20%.

35. A sells an article which costs him Rs. 400 to B at a profit of 20%. B then sells it to C, making a profit of 10% on the price he paid to A. How much does C pay B?

Sol: C.P. for B = 120% of Rs. 400 = Rs. 120 100  x 400  = Rs. 480.

C.P. for C = 110% of Rs. 480 = Rs. 110 100  x 480  = Rs. 528.

36.Jacob bought a scooter for a certain sum of money. He spent 10% of the cost on repairs and sold the scooter for a profit of Rs. 1100. How much did he spend on repairs if he made a profit of 20%?

Sol: Let the C.P. be Rs. x. Then, 20% of x = 1100

20 100  x x = 1100

x = 5500.

C.P. = Rs. 5500, Expenditure on repairs = 10%.

Actual price = Rs. 100 110  x 5500  = Rs. 5000.

Expenditure on repairs = Rs. (5500 – 5000) = Rs. 500.

37.Some articles were bought at 6 for Rs. 5 and sold at 5 for Rs. 6. Gain percent is

Sol: Suppose, number of articles bought = L.C.M. of 6 and 5 = 30.

C.P. of 30 articles = Rs. 5 6  x 30  = Rs. 25. S.P. of 30 articles = Rs. 6 5  x 30  = Rs. 36.

Gain% = 11 25  x 100 % = 44%.

38. In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit ? Sol: Let C.P. = Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420. New C.P. = 125% of Rs. 100 = Rs. 125; New S.P. = Rs. 420. Profit = Rs. (420 - 125) = Rs. 295.    Required percentage = 295 420  x 100 % = 1475 21 % = 70%. 39.An article was sold for Rs. 144. If the percentage of profit was numerically equal to the cost price, the cost of the article was : Sol:  Let C.P. = Rs. x, Profit% = x% and S.P. = Rs. 144.  x = 100 (100 + x)  x 144 x2 + 100x = 14400 x2 + 100x - 14400 = 0.  x2 + 180x - 80x - 14400 = 0   (x + 180) (x - 80) = 0   x = 80. 40.A vendor loses the selling price of 4 oranges on selling 36 oranges, His loss percent is : Sol: (C.P. of 36 mangoes) - (S.P. of 36 mangoes) - Loss = (S.P. of 4 mangoes)   S.P. of 40 mangoes = C.P. of 36 mangoes. Let C.P. of each mango be Re. 1. C.P. of 40 mangoes = Rs. 40; S.P. of 40 mangoes = Rs. 36.   Loss% = 4 40  x 100 % = 10%. 41. By selling a pen for Rs. 15, a man loses one-sixteenth of what it costs him. The cost price of the pen is : Let the C.P. be Rs. x. Then, x - 15 = x 16 x - x 16  = 15 15x 16  = 15 x = 16.  C.P. = Rs. 16. 42.A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%? C.P. of 6 toffees = Re. 1. S.P. of 6 toffees = 120% of Re. 1 = Rs. 6 5 For Rs. 6 5 , toffees sold = 6. For Re. 1, toffees sold = 6 x 5 6  = 5. 43. A man buys eggs at 2 for Re. 1 and an equal number at 3 for Rs. 2 and sells the whole at 5 for Rs. 3. His gain or loss percent is: Sol: Suppose he buys 6 eggs of each kind. C.P. of 12 eggs = Rs. 1 2  x 6 + 2 3  x 6  = Rs. 7, S.P. of 12 eggs = Rs. 3 5  x 12  = Rs. 7.20.   Gain = 0.20 7  x 100 % = 2 6 7 %. 44. A grocer sells rice at a profit of 10% and uses weights which are 20% less than the market weight. The total gain earned by him will be : Sol: Let us consider a packet of rice marked 1 kg. Its actual weight is 80% of 1000 gm = 800 gm. Let C.P. of each gm be Re. 1. Then, C.P. of this packet = Rs. 800. S.P. of this packet = 110% of C.P. of 1 kg = Rs. 110 100  x 1000  = Rs. 1100.   Gain% = 300 800  x 100 % = 37.5% 45. Profit earned by selling an article for Rs. 1060 is 20% more than the loss incurred by selling the article for Rs. 950. At what price should the article be sold to earn 20% profit? Sol: Let C.P. be Rs. x. Then, (1060 - x) = 120 100  (x - 950) 106000 - 100x = 120x - 120 x 950  220x = 220000   x = 1000.   Desired S.P. = Rs. 120 100  x 1000  = Rs. 1200. 46.The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is : Let C.P. of the article be Rs. x. Then, required ratio = 104% of x 106% of x = 104 106 = 52 53  = 52 : 53. 47.A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.50 per kg. What will be his gain percentage? C.P. of 1 kg = Rs. 420 70  = Rs. 6. S.P. of 1 kg = Rs. 6.50.  Gain % = 0.50 6  x 100 % = 25 3 % = 8 1 3 % 48. A house and a shop were sold for 1 lakh each. In this transaction, the house sale resulted into 20% loss whereas the shop sale resulted into 20% profit. The entire transaction resulted in:  Sol: Total S.P. = Rs. 2 lakh. C.P. of house = Rs. 100 80  x 1  lakh = Rs. 5 4  lakh. C.P. of shop = Rs. 100 120  x 1  lakh = Rs. 5 6  lakh. Total C.P. = Rs. 5 4 + 5 6  lakh = Rs. 25 12  lakh.  Loss = Rs. 25 12  - 2  lakh = Rs. 1 12  lakh. 49.A cloth merchant sold half of his cloth at 20% profit, half of the remaining at 20% loss and the rest was sold at the cost price. In the total transaction, his gain or loss will be: Let C.P. of whole be Rs. x. C.P. of 1 2  stock = Rs. x 2 , C.P. of 1 4  stock = Rs. x 4 . Total S.P. = Rs. 120% of x 2 + 80% of x 4 + x 4  = Rs. 3x 5 + x 5 + x 4  = Rs. 21x 20 Gain = Rs. 21x 20  - x  = Rs. x 20   Gain% = x 20 x 1 x  x 100 % = 5% 50. The cost price of 19 articles is equal to the selling price of 16 articles. Gain percentage is : Sol: Let C.P. of each article be Re. 1. Then, C.P. of 16 articles = Rs. 16; S.P. of 16 articles = Rs. 19.  Gain % = 3 16  x 100 % = 18 3 4 % 51.An article when sold at a again of 5% yields Rs. 15 more than when sold at a loss of 5%. Its cost price would be: Let C.P. be Rs. x. Then, 105 100 x - 95 100 x = 15 10x 100  = 15    x = 150. 52. By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg, a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost? Let the cost of the other brand be Rs. x per kg. C.P. of 5 kg = Rs. (2 x 200 + 3 x x) = Rs. (400 + 3x) S.P. of 5 kg = Rs. (5 x 177) = Rs. 885. 885 - (400 + 3x) 400 + 3x  x 100 = 18 485 - 3x 400 + 3x = 9 50  24250 - 150x = 3600 + 27x   177x = 20650   x = 350 3  = 116 2 3 So, cost of the other brand = Rs. 116.66. 53.A fruit seller sells mangoes at the rate of Rs. 9 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5% Sol: 80 : 9 = 105 : x or x = 9 x 105 80  = 11.81 Hence, S.P. per kg = Rs. 11.81 54.At what profit percent must an article be sold so that by selling at half that price, there may be a loss of 30%? Let S.P. = Rs. x. New S.P. = Rs. x 2 , Loss = 30%. So, C.P. = Rs. 100 70 x x 2  = Rs. 5x 7 . Profit = Rs. x - 5x 7  = Rs. 2x 7   Profit% = 2x 7 x 7 5x  x 100 % = 40%. 55.If on selling 12 notebooks, a seller makes a profit equal to the selling price of 4 notebooks, what is his percent profit? (S.P. of 12 notebooks) - (C.P. of 12 notebooks) = (S.P. of 4 notebooks)   C.P. of 12 notebooks = S.P. of 8 notebooks. Let C.P. of each notebook be Re. 1. Then, C.P. of 8 notebooks = Rs. 8; S.P. of 8 notebooks = Rs. 12.   Gain% = 4 8  x 100 % = 50%. 56.A trader buys a chair for Rs. 600 and sells it for Rs. 765 at a credit of 4 months. Reckoning money worth 6% p.a., his gain percent is:  Sol: C.P. = Rs. 600 + 600 x 6 x 4 100 x 12  = Rs. 612. Gain = Rs. (765 - 612) = Rs. 153.  Gain% = 153 612  x 100 % = 25% 57. On an order of 5 dozen boxes of a consumer product, a retainer receives an extra dozen free. This is equivalent to allowing him a discount of : Clearly, the retailer gets 1 dozen out of 6 dozens free.    Equivalent discount = 1 6  x 100 % = 16 2 3 % 58. 100 oranges are bought at the rate of Rs. 350 and sold at the rate of Rs. 48 per dozen.The percentage of profit or loss is :

Sol:

C.P. of 1 orange = Rs. 350 100  = Rs. 3.50. S.P. of 1 orange = Rs. 48 12  = Rs. 4.

Gain % = 0.50 3.50  x 100 % = 100 7 % = 14 2 7 %

59. The profit earned by selling an article for Rs. 900 is double the loss incurred when the same article is sold for Rs. 450. At what price should the article be sold to make 25% profit?

Let C.P. = Rs. x. Then, 900 - x = 2 (x - 450)   3x = 1800   x = 600.

Required S.P. = 125% of Rs. 600 = Rs. 125 100  x 600  = Rs. 750.

60.A dishonest dealer uses a scale of 90 cm instead of a metre scale and claims to sell at cost price. His Profit is :

Gain% = 10 90  x 100 % = 11 1 9 %

61.By selling an article for Rs. 100, a man gains Rs. 15. Then, his gain% is:

S.P. = Rs. 100, gain = Rs. 15.

C.P. = Rs. (100 - 15) = Rs. 85.

Gain% = 15 85  x 100 % = 300 17 % = 17 11 17 %

62.A man gains 20% by selling an article for a certain price. If he sells it at double the price, the percentage of profit will be

Let C.P. = Rs. x. Then, S.P. = Rs. (120% of x) = Rs. 6x 5

New S.P. = Rs. 2 x 6x 5  = Rs. 12x 5 . Profit = Rs. 12x 5  - x  = Rs. 7x 5

Profit% = 7x 5 x 1 x  x 100 % = 140%.

63.The difference between the cost price and sale price of an article is Rs. 240. If the profit is 20%, the selling price is :

Let the C.P. be Rs. x.

Then, S.P. = 120% of Re. x = Rs. x x 120 100  = Rs. 6x 5

6x 5  - x = 240  x = 1200.

S.P. = Rs. 6 5  x 1200   = Rs. 1200.

64.10% loss on selling price is what percent loss on the cost price?

Let S.P. = Rs. 100. Then, Loss = Rs. 10, C.P. = Rs. (100 + 10) = Rs. 110.

Loss% = 10 110  x 100 % = 9 1 11 %

65.A shopkeeper sold an article for Rs. 2090.42. Approximately, what will be the percentage profit if he sold that article for Rs. 2602.58?

Profit = Rs. (2602.58 - 2090.42) = Rs. 512.16

Profit = 512.16 2090.42  x 100 % = 512160 209042  x 10 % = 24.5% = 25%

66.A man purchased a box full of pencils at the rate of 7 for Rs. 9 and sold all of them at the rate of 8 for Rs. 11. In this transaction, he gained Rs. 10. How many pencils did the box contain?

Suppose, number of pencils bought = L.C.M. of 7 and 8 = 56.

C.P. of 56 pencils = Rs. 9 7  x 56  = Rs. 72. S.P. of 56 pencils = Rs. 11 8  x 56  = Rs. 77.

Now, Rs. 5 are gained on 56 pencils.

So, Rs. 10 are gained on 56 5  x 10  = 112 pencils.

67.If books bought at prices ranging from Rs. 200 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 425, what is the greatest possible profit that might be made in selling eight books?

Least C.P. = Rs. (200 x 8) = Rs. 1600.

Greatest S.P. = Rs. (425 x 8) = Rs. 3400.

Required profit = Rs. (3400 – 1600) = Rs. 1800.

68.A shopkeeper sells one transistor for Rs. 840 at a gain of 20% and another for Rs. 960 at a loss of 4%. His total gain or loss percent is :

C.P. of 1st transistor = Rs. 100 120  x 840  = Rs. 700.

C.P. of 2nd transistor = Rs. 100 96  x 960  = Rs. 1000.

So, total C.P. = Rs. (700 + 1000) = Rs. 1700.

Total S.P. = Rs. (840 + 960) = Rs. 1800.

Gain % = 100 1700  x 100 % = 5 15 17 %

69. A house worth Rs. 1,50,000 is sold by X to Y at 5% profit. Y sells the house back to X at 2% loss. Then, in the entire transaction:

Money spent by X = Rs. 150000.

Money received by X = 105% of Rs. 150000 = Rs. 157500

C.P. to X = 98% of Rs. 157500 = Rs. 154350.

X gains Rs. (157500 - 154350) = Rs. 3150.

70. If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is :

Let C.P. be Rs. x. Then, 5% of x = (350 - 340) = 10 x 20  = 10   x = 200.

71.A man bought apples at the rate of 8 for Rs. 34 and sold them at the rate of 12 for Rs. 57. How many apples should be sold to earn a net profit of Rs. 45

C.P. of 1 apple = Rs. 34 8  = Rs. 4.25. S.P. of 1 apple = Rs. 57 12  = Rs. 4.75.

Profit on each apple = Re. 0.50.

Number of apples required = 45 0.50  = 90.

72. Arun purchased 30 kg of wheat at the rate of Rs. 11.50 per kg and 20 kg of wheat at the rate of Rs. 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should he sell the mixture to make 30% profit?

C.P. of 50 kg wheat = Rs. (30 x 11.50 + 20 x 14.25) = Rs. (345 + 285) = Rs. 630

S.P. of 50 kg wheat = 130% of Rs. 630 = Rs. 130 100  x 630   = Rs. 819.

S.P. per kg = Rs. 819 50  = Rs. 16.38 = Rs. 16.30.