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Business transactions have now-a-days become common feature of life. When a person deals in the purchase and sale of any item, he either gains or loses some amount generally. The aim of any business is to earn profit. The commonly used terms in dealing with questions involving sale and purchase are:

Cost Price The cost price of an article is the price at which an article has been purchased. It is the abbreviated as C.P.

Selling Price The selling price of an article is the price at which an article has been sold. It is abbreviated as S.P. Profit or Gain If the selling price of an article is more that the cost price, there is a gain or profit.

Thus, Profit or Gain = S.P- C.P.

Loss If the cost price of an article is greater than the selling price, the suffers a loss. Thus, Loss = C.P- S.P.

Note that profit and loss are always calculated with respect to the cost price of the item. Illustration 1. (i)If C.P. = Rs. 235, S.P. = Rs. 240, then profit = ?

(ii) If C.P. = Rs. 116, S.P. = Rs. 107, then loss = ? Solution (i) Profit = S.P.- C.P. =Rs. 240- 235 =Rs.5.

(ii) Loss = C.P.- S.P. = Rs. 116- 107 =Rs.9.

SOME BASIC FORMULAE 1. Gain on Rs. 100 is Gain per cent

Gain% = (Gain  100)/C.P

Loss on Rs. 100 is Loss per cent

Loss% = (Loss  100)/C.P

Illustration 2 The cost price of a shirt is Rs. 200 and selling price is Rs. 250. Calculate the % profit. Solution We have, C.P. = Rs. 200, S.P = Rs. 250.

Profit = S.P.- C.P. = 250- 200 =Rs.50.

 Profit% = profit 100/ C.P = 50 100/ 250 = 25%

Illustration 3 Anu bought a necklace for Rs. 750 and sold it for Rs. 675. Find her percentage loss. Solution Here, C.P. = 750, S.P. = Rs. 675.

Loss= C.P- S.P. = 750-675 = Rs. 75.

 Loss% = Loss  100/ C.P = 75 100/ 750 = 10%

2. When the selling price and gain% are given:

C.P = 100S.P / (100+Gain%)

3. When the cost and gain per cent are given;

S.P = (100+Gain%)C.P/ 100

4. When the cost and loss per cent are given:

S.P = (100-Loss%)C.P / 100

5. When the selling price and loss per cent are given:

C.P =(100)S.P / (100-Loss%)

Illustration 4 Mr. Sharma buys a cooler for Rs. 4500. For how much should he so that there is a gain of 8%? Solution We have, C.P. = Rs. 4500, gain% = 8%

S.P = (100+Gain%/100)C.P.

= (100+ 8/ 100)  4500

Illustration 5 By selling a fridge Rs. 7200, Pankaj loses 10%. Find the cost price of the fridge. Solution We have, S.P. = Rs. 7200, loss% = 10%.

 C.P =(100/100-Loss%)S.P.

= (100/100-10)  7200

100/90  7200= Rs. 8000.

Illustration 6 By selling a pen for Rs. 99, Mohan gains 12 ½ %. Find the cost price of the pen. Solution Here, S.P. = Rs. 99, gain% = 12 ½% or 25/2%.

C.P =(100/100+Gain%)S.P.

= (100/100+25/2) 99

= (1002/ 225) 99 =Rs. 88

SOME USEFUL SHORT-CUT METHODS

1. If a man buys x items for Rs. y and sells z items for Rs. w, then the gain or loss per cent made by him is

(xw/zy -1)  100%.

Explanation

S.P. of z items = Rs. w S.P. of x items = Rs. w/z x Net profit =w/z x-y.

% profit = w/z x-y/y 100%

i.e.(xw/zy -1) 100,

which represent loss, if the result is negative.

Note: In the case of gain per cent the result obtained bears positive sign whereas in the case of loss per cent the result obtained bears negative sign.

How to remember:

1. Cross-multiply the numbers connected by the arrows (xw and zy)

2. Mark the directon of the arrows for crossmultiplicaton. The arrow going down forms the numerator while the arrow going up forms the denominator (xw/ zy).

Illustration 7 If 11 oranges are bought for Rs. 10 and sold at 10 for Rs. 11 what is the gain loss%? Solution

% profit= (xw/zy -1)  100%

= (1111/1010-1) 100%

= 21/100 100% = 21%

Illustration 8 A fruit seller buys apples at the rate of Rs 12 per dozen and sells them at the rate of 15 for Rs.12. Find his percentage gain or loss.

Solution

% gain or loss = (xw/ zy -1)  100%

= (12 12/15 12 -1) 100%

= -36/144  100% = -25%

Since the sign is –ve, there is a loss of 25%.

2. If the cost price of m articles is equal to the selling price of n articles, then

% gain or loss = ( m-n/n) 100

[If m > n, it is gain and if m<n, it is loss]

Let the C.P. of one article be Re.1  C.P. of m articles = Rs. m1=Rs. m S.P. of n articles = Rs. m  S.P. of 1 articles = Rs. m/n Profit on 1 article = Rs.(m/n-1) i.e. Rs. (m-n/n)  %profit = m-n/n  100/1 i.e.(m-n/n) 100.

Illustration A shopkeeper professes to sell his goods on cost price but uses 800 gm, instead of 1kg. What is his gain %?

Solution Here, cost price of 1000 is equal to selling price of 800 gm.

 % gain = (m-n/n) 100

= (1000-800/800)  100

= 200/800100 =25%

Illustration 10 If the selling price of 12 articles is equal to the cost price of 18 articles, what is the profit %? Solution Here, m = 10, n =12

 Profit %= (m-n/n) 100

(18-12/12) 100

= 6/12 100= 50%

EXERCISE

1. By selling a watch for Rs.495, a shopkeeper incurs a loss of 10%. Find the cost price of the watch for the shopkeeper.

1. 545/- 2. 550/- 3. 555/- 4. None

2. A cellular phone when sold for Rs.4600 fetches a profit of 15%. Find the cost price of the cellular phone.

1. 4300/- 2. 4150/- 3. 4000/- 4. 4500/-

3. A machine costs Rs.375. If it is sold at a loss of 20%, what will be its cost price as a percentage of its selling price?

1. 80% 2. 120% 3. 110% 4. 125%

4. A shopkeeper sold goods for Rs.2400 and made a profit of 25% in the process. Find his profit per cent if he had sold his goods for Rs.2040.

1. 6.25% 2. 7% 3. 6.20% 4. 6.5%

5. By selling bouquets for Rs.63, a florist gains 5%. At what price should he sell the bouquets to gain 10% on the cost price?

1. 66/- 2. 69/- 3. 72/- 4. 72.50/-

6. The cost price of a shirt and a pair of trousers is Rs.371. If the shirt costs 12% more than the trousers, find the cost price of the trouser.

1. 125/- 2. 150/- 3. 175/- 4. 200/-

7. ******A pet shop owner sells two puppies at the same price. On one he makes a profit of 20% and on the other he suffers a loss of 20%. Find his loss or gain per cent on the whole transaction.

1. Gain of 4% 2. No profit no loss 3. Loss of 10% 4. Loss of 4%

8. The marked price of a table is Rs.1200, which is 20% above the cost price. It is sold at a discount of 10% on the marked price. Find the profit per cent.

1. 10% 2. 8% 3. 7.5% 4. 6%

9. *****A shopkeeper marks the price of an articles at Rs.80. Find the cost price if after allowing a discount of 10% he still gains 20% on the cost price.

10. ****The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25% then the value of ―x‖ is.

1. 25 2. 18 3. 16 4. 15

11. A dozen pairs of gloves quoted at Rs.80 are available at a discount of 10%. Find how many pairs of gloves can be bought for Rs.24.

1. 4 2. 5 3. 6 4. 8

12. ******Find a single discount equivalent to the discount series of 20%, 10%, 5%.

1. 30% 2. 31.6% 3. 68.4% 4. 35%

13. *****How much percent more than the cost price should a shopkeeper mark his goods, so that after allowing a discount of 12.5% he should have a gain of 5% on his outlay?

1. 9.375 2. 16.66% 3. 20% 4. 25%

14. ****In order to maintain the price line, a trader allows a discount of 10% on the marked price of goods in his shop. However, he still makes a gross profit of 17% on the cost price. Find the profit percent he would have make on the selling price had he sold at he marked price.

1. 23.07 2. 30% 3. 21.21% 4. 25%

15. *****qq A whole-seller allows a discount of 20% on the list price to a retailer. The retailer sells at 5% discount on the list price. If the customer paid Rs.38 for an article, what profit is made by the retailer?

1. 10/- 2. 8/- 3. 6/- 4. None

16. *****The cost of production of a cordless phone set in 2002 is Rs.900, divided between material, labor and overheads in the ratio 3:4:2. If the cordless phone set is marked at a price that gives a 20% profit on the component of price accounted for by labor, what is the marked price of he set?

1. 980/- 2. 1080/- 3. 960/- 4. None

17. *****A shopkeeper sells an article at a profit of 10% and uses weights which are 20% less than the arrival weight the total gain earned by him will be

1. 30% 2. 88% 3. 37.5% 4. None of these

18. A man sells 5 articles forRs.15 and makes a profit of 20%. Find his gain or loss percent if he sells 8 such articles for Rs.18.40.

1.2.22% profit 2. 2.22% loss 3. 8% loss 4. 8% profit

19. The cost price of 50 mangoes is equal to the selling price of 40 mangoes. Find the percentage profit?

1. 20% 2. 25% 3. 30% 4. None

20. A makes an article for Rs.120 and sells it to B at a profit of 25%. B sells it to C who sells it for Rs.198, making a profit of 10%. What profit percent did B make?

1. 25% 2. 20% 3. 16.66% 4. 15%

21. *****A reduction of 10% in the price of sugar enables a housewife to buy 6.2kg more for Rs.279. Find the reduced price per kilogram.

1. 5/- 2. 4.5% 3. 4.05% 4. None

22. A man buys 50 kg of oil at Rs.10 per kilogram and another 40 kg of oil at Rs.12 kilogram and mixes them. He sells the mixture at the rate of Rs.11 per kilogram. What will be his gain percent if he is able to sell the whole lot?

1. 100/98% 2. 100(10/49)% 3. 10(1/49)% 4. None

23. *A shopkeeper sells sugar in such a way that the selling price of 950 gm is the same as the cost price of one kilogram. Find his gain percent.

1. 100/17% 2. 150/17% 3. 5(5/19)% 4. 1/19%

24. *A sold a table to B at a profit of 15%. Later on, B sold it back to A at a profit of 20%, thereby gaining Rs.69. How much did A pay for the table originally?

25. A color TV and a VCP were sold for Rs.12, 000 each. The TV was sold at a loss of 20% whereas the VCP was sold at a gain of 20%. Find gain or loss in the whole transaction.

1. 1200/- loss 2. 1000/- loss 3. 960/- loss 4. 1040/- loss

26. *A man sells a TV set for Rs.3450 and makes a profit of 15%. He sells another TV at a loss of 10%. If on the whole, he neither gains nor loses, find the selling price of the second TV set.

1. 4000/- 2. 4400/- 3. 4050/- 4. 4500/-

27. A man sells an article at 5% above its cost price. if he had bought it at 5% less than what he paid for it and sold it for Rs.2 less, he would have gained 10%. Find the cost price of the article.

1. 500/- 2. 360/- 3. 425/- 4. 400/-

28. A briefcase was sold at a profit of 10%. If its cost price was 5% less and it was sold for Rs.7 more, the gain would have been 20%. Find the cost price of the briefcase.

1. 175/- 2. 200/- 3. 225/- 4. 160/-

29. *A man buys two cycles for a total cost of Rs.900. By selling one for 4/5 of its cost and other for 5/4 of its cost, he makes a profit of Rs.90 on the whole transaction. Find the cost price of lower priced cycle?

1. 360/- 2. 250/- 3. 300/- 4. 420/-

30. A merchant bought two transistors, which together cost him Rs.480. He sold one of them at a loss of 15% and other at a gain of 19%. If the selling price of both the transistors are equal, find the cost of the lower priced transistor.

1. 300/- 2. 180/- 3. 200/- 4. 280/-

31. Two dealers X and Y selling the same model of refrigerator mark them under the same selling prices. X gives successive discounts of 25% and 5% and Y gives successive discounts of 16% and 12%. From whom is it more profitable to purchase the refrigerator?

1. From Y 2. From X 3. Indifferent between the two 4. cannot be determined

32. A firm dealing in furniture allows 4% discount on the marked price of each item. What price must be marked on a dining table that cost Rs.400 to assemble, so as to make a profit of 20%.

1. 475/- 2. 480/- 3. 500/- 4. 520/-

33. A shopkeeper allows a discount of 12.5% on the marked price of a certain article and makes a profit of 20%. If the article cost the shopkeeper Rs.210, what price must be marked on the article?

1. 280/- 2. 288/- 3. 300/- 4. None

34. `A watch dealer pays 10% custom duty on a watch that costs Rs.250 abroad. For how much should he mark it, if he desires to make a profit of 20% after giving a discount of 25% to the buyer?

1. 400/- 2. 440/- 3. 275/- 4. 330/-

35. *A dishonest dealer professes to sell at cost price but uses a 900 gram weight instead of 1 kg. Weight. Find the percent profit to the dealer.

In document CÓDIGO ORGÁNICO GENERAL DE PROCESOS (página 148-151)