# Profit and Loss Formulas and Short Tricks

for SSC CGL 2017

# Topic: Profit and loss Short Tricks

__Cost Price __

The price, at which an article is purchased, is called its cost price, abbreviated as C.P.

__Selling Price__

The price, at which an article is sold, is called its selling prices, abbreviated as S.P.

- Profit/gain= SP – CP
- Profit% = Profit/(C P)×100
- S P= (100+gain % )/100 ×C P
- C P= 100/(100+gain %)×S P

__Loss____: __

If the overall Cost Price exceeds the selling price of the buyer then he is said to have incurred loss.

- Loss= C P – S P
- Loss% = LOSS/(C P)×100
- S P= (100-loss %)/100×C P
- C P= 100/(100-loss %)×S P

__Profit and Loss Based on Selling Price__

To find the profit and the cost when the selling price and the percent profit are given, multiply the selling price by the percent profit and subtract the result from the selling price.

Example: A toy is sold for Rs. 6.00 at a profit of 25% of the selling price. Separate this selling price into cost and profit.

Answer :

Selling price x % profit = profit.

Selling price = profit + cost.

6.00 x .25 = 1.50, profit.

6.00 – 1.50 = 4.50, cost.

To find the loss and the cost when the selling price and the percent loss are given, multiply the selling price by the percent loss and subtract the result from the selling price.

Example: At a sale, neckties selling at Rs. 50.00 are sold at a loss of 60% of selling price. What is the loss and the original cost?

Selling price x % loss = loss.

Selling price + loss = cost.

50.00 x .60 = 30.00, loss.

50.00 – 30.00 = 20.00, cost.

To find the selling price when the cost and the percent loss are given, add the percent loss to 100% and divide the cost by this sum.

Example: Socks that cost 7.00 per pair were sold at a loss of 25% of selling price. What was the selling price?

Answer: Cost / (100% + % loss) = selling price.

7.00 / 1.25 = 5.60, selling price.

To find the selling price when the profit and the percent profit are given, or to find the selling price when the loss and the percent loss are given, divide the profit or loss by the percent profit or loss.

Note: This rule should be compared with the one under Profit and Loss Based on Cost. The two rules are exactly similar except that in one case 100% represents cost while in the other case 100% represents selling price.

Example: A kind of tape is selling at a profit of 12% of selling price, equal to 18 per yard. What is the selling price of the tape?

Answer: Profit / % profit = selling price.

18 /.12 = 1.50 selling price.

To find the percent profit or loss, divide the amount gained or lost by the selling price.

Example: A candy bar sells for 1.30 at a profit of 65. What percent of the profit on selling price does this represent?

Answer: Gain / selling price = % profit.

65 / 1.30 = .5 or 50% profit.

__Profit and Loss Based on Cost Price__

To find the percent gain or loss, divide the amount gained or lost by the cost and multiply it by 100.

Example: A toy that cost 80 rupees is sold at a profit of 20 rupees. Find the percent or rate of profit.

Answer:

Gain/cost × 100 = % profit.

20/80 × 100 = 25%. – Answer

To find the loss and the selling price when the cost and the percent loss are given, multiply the cost by the percent and subtract the product from the cost.

Example: A damaged chair that cost Rs.110 was sold at a loss of 10%. Find the loss and the selling price.

Answer:

Cost x percent loss = loss.

110 x 1/10 = 11, loss.

Cost – loss = selling price.

110 – 11 = 99, selling price.

__Mark-up Price__

Generally the SP is less than the marked price (MP) the difference MP – SP is known as discount, D.

Discount = M P – S P

Discount %, D% = (Discount) / (M P) ×100

To reduce percent loss on cost to percent loss on selling price, divide percent loss on cost by 100% minus percent loss on cost.

Example: 20% loss on cost is what percent loss on selling price?

Answer:

% loss on cost / (100% – % loss on cost) = % loss on selling price.

0.20 / 80 = .0025 or 25% loss on selling price

To reduce percent loss on selling price to percent loss on cost, divide percent loss on selling price by 100% plus percent loss on selling price.

Example: 20% loss on selling price is what percent loss on cost?

Answer:

% loss on selling price / (100% + % loss on selling price) = % loss on cost.

.20 / 1.20 = .16666 or .16.67% loss on cost.

To reduce percent mark-up (percent profit on cost) to percent profit on selling price, divide percent mark-up by 100% plus percent mark-up.

Example: A coat marked up 60% carries what percent of profit on selling price?

Answer : % profit on cost / ( 100% + % profit on cost ) = % profit on selling price.

.60 / 1.60 = .375 or 37.5% on selling price.

Here we are providing you all the types of questions that have been asked in SSC Exams and How to solve it in an Easy way with Grade Stack methods:-

__Type 1: __

The cost price of 40 articles is the same as the selling price of 25 articles. Find the gain per cent. (CGL-2012)

(a) 65%

(b) 60%

(c) 15%

(d) 75%

Answer: (b) Gain per cent

=(40-25)/25×100

=15/25×100=60%

Grade Stack methods

In Above question We take x = 40 , y = 25

Then Gain % = (x –y) x 100/ y

__Type2: __

Bananas are bought at the rate of 6 for Rs. 5 and sold at the rate of 5 for Rs. 6. Profit per cent is: (CGL-2004)

(a) 36%

(b) 42%

(c) 44%

(d) 48%

Answer : (c) To avoid fraction, let the number of bananas bought

LCM of 5 and 6 = 30

CP of 30 bananas

= 5 x 5 = Rs. 25

SP of 30 Bananas = 6 x 6

= Rs. 36

Profit = Rs. (36-25) = Rs. 11

Profit %

= 11/25×100=44%

Grade Stack Method

[(6 x 6 -5x 5)/ (5 x 5)] x 100 = 44%

__Type 3:__

A man bought oranges at the rate of 8 for Rs 34 and sold them at the rate of 12 for Rs. 27. How many oranges should be sold to earn a net profit of Rs 45? (CGL-2011)

(a) 90

(b) 100

(c) 135

(d) 150

Answers: (a) Let the man buy 24 (LCM of 8 and 12) oranges.

C.P. of 24 oranges = 34/8 ×24 = Rs. 102

S.P. of 24 oranges = 27/12×24= Rs. 114

Gain = 114 – 102 = Rs. 12

Rs. 12 = 24 oranges

Rs. 45 = 24/12×45= 90 oranges

__Type 4: __

A shopkeeper earns a profit of 12% on selling a book at 10% discount on printed price. The ratio of the cost price to printed price of the book is ?(CGL-2013)

(a) 45 : 56

(b) 50 : 61

(c) 90 : 97

(d) 99 : 125

Answer: (a) C.P. of the book = Rs. x

Printed price = Rs. y

(y×90)/100=x × 112/100

x/y=90/112=45/56

__Type 5: __

A dealer sold two types of goods for Rs 10,000 each. On one of them, he lost 20% and on the other he gained 20%. His gain or loss per cent in the entire transaction was (CGL-2012)

(a) 2% loss

(b) 2% gain

(c) 4% gain

(d) 4% loss

Answers: (d) Here, S.P. is same, Hence there is always a loss. Loss per cent =(20×20)/100=4%

Gradestack Trick

Loss % = (n^2)/100= (20)^2/100= 4%

Where n= 20

__Type 6: __

On selling an article for Rs170, a shopkeeper loses 15%. In order to gain 20%, he must sell that article at rupees: (CGL-2013)

(a) 215.50

(b) 212.50

(c) 240

(d) 210

Answer ; (c) C.P. of article = (200×120)/100 = Rs. 240

__Type 7:__

An article is sold at a loss of 10%. Had it been sold for Rs. 9 more, there would have been a gain of 12 1/2% on it. The cost price of the article is (CGL – 2002)

(a) Rs. 40

(b) Rs. 45

(c) Rs. 50

(d) Rs. 35

Answers: (a) Let the cost price of the article = Rs. x

S.P. at 10% loss

= x×90/100= Rs. 9x/10

- at 12 1/2 % gain

x × (100+12 1/2)/100 = Rs. 225x/200

According to the question

9x/10 + 9 = 225x/200

180x + 1800 = 225x

x = Rs. 40

__Type 8: __

A sells a suitcase to B at 10% profit. B sells it to C at 30% profit. If C pays Rs 2860 for it, then the price at which a bought it is (CGL-2013)

(a) 1000

(b) 1600

(c) 2000

(d) 2500

Answer: (c) If the C.P. of the suitcase for A be Rs. x, then

x ×110/100×130/100=2860

x=(2860×100×100)/(110×130) = Rs. 2000

__Type 9:__

Arun marks up the computer he is selling by 20% profit and sells them at a discount of 15%. Arun’s net gain percent is

(CGL-2013)

(a) 4

(b) 2

(c) 3.5

(d) 2.5

Answer (b)

Gradestack method:

r1 = 20 , r2 = 15

Formula = r1 – r2 – (r1 x r2)/100

(20-15-(20×15)/100)

= 20 -18 = 2%

__Type10:__

A tradesman sold an article at a loss of 20%. If the selling price had been increased by Rs. 100, there would have been a gain of 5%. The cost price of the article was: (CGL-2004)

(a) Rs. 200

(b) Rs. 25

(c) Rs. 400

(d) Rs. 250

Answer (c) Let the C.P. of article be Rs. x.

105% of x – 80% of x = Rx. 100

25% of x = Rx. 100

x = Rs. (100×100)/25

= Rs. 400

Q1. A man wanted to sell an article with 20% profit; but he actually sold at 20% loss for Rs 480. At what price (Rs) he wanted to sell it to earn the profit?

a) 720 b) 840 c) 600 d) 750

Q2. The cost price of 36 books is is equal to the selling price of 30 books. The gain per cent is:

a) 20% b) 50/3 % c) 18% d) 24%

Q3 A person sells two machines at Rs 396 each. One one he gains 10% and on the other he loses 10%. His profit or loss in the whole transaction is:

a) No gain no loss b) 1% loss c) 1% profit d) 8% profit

Profit and Loss

Q4. A house and a shop were sold for Rs 1 lakh each. In this transaction, the house sale resulted into 20% loss whereas the shop sale into 20% profit. The entire transaction resulted in

a) No loss no gain b) gain of Rs 1/24 lakh c) Loss of Rs 1/12 lakh d) Loss of Rs 1/18 lakh

Q5. A sells a bicycle to B at a profit of 20%. B sells it to C at a profit of 25%. If C pays Rs 225 /- for it, the cost price of the bicycle for A is:

a) Rs 110/- b) Rs 125 /- c) Rs 120 /- d) Rs 150/-

Q6. 12 copies of a book were sold for Rs 1800/- thereby gaining cost-price of 3 copies. The cost price of a copy is:

a) Rs 120 b) 150 c) RS 1200 d) Rs 1500

Q7. If a man estimates his loss as 20% of the selling price, then his loss per cent is:

a) 20% b) 25% c) 40/3% d) 50/3%

Q8. If I would have purchased 11 articles for Rs 1o and sold all the articles at the rate of 10 for Rs 11, the profit per cent would have been:

a) 10% b) 11% c) 21% d) 100%

Q9. An article is sold at a loss of 10%. Had it been sold for Rs 9 more, there would have been a gain of 25/2% on it. The cost price of the article is:

a) Rs40 b) RS 45 c) Rs 50 d) RS 35

Q10. A man buys a cycle for Rs 1400 and sells it at a loss of 15%. What is the selling price of the cycle?

a) Rs 1202 b) Rs 1190 c) Rs 1160 d) RS 1000

Profit and Loss

Q11. The ratio of cost price and selling price is 5: 4, the loss percent is:

a) 20% b0 25% c) 405 d) 50%

Q12.A person buys some pencils at 5 for a rupee and sells them at 3 for a rupee. His gain percent will be:

a) 200/3 b) 230/3 c) 170/3 d) 140/3

Q13. If selling price of an article is 8/5 times its cost price, the profit per cent on it is

a) 120% b) 160% c) 40% d) 60%

Q14. The price of coal is increased by 20%. By what per cent a family should decrease its consumption so that expenditure remains same?

a) 40% b) 70/3% c) 20% d) 50/3%

Q15: 100 oranges are bought for Rs 350 and sold at the rate of Rs 48 per dozen. The percentage of profit or loss is:

a) 15% loss b) 15% gain c) 100/7% loss d) 100/7% profit

Q16. A reduction of 20% in the price of salt enables a purchaser to obtain 4 kg more for Rs 100. The reduced price of salt per kg is:

a) Rs 4 b) Rs 5 c) Rs 6.25 d) Rs 6.50

Q17. A person sells a table at a profit of 10%. If he had bought the table at 5% less cost and sold for rs 80 more, he would have gained 20%. The cost price of the table is

a) Rs 3200 b) Rs 2500 c) Rs 2000 d) Rs 200

Q18. A person sells an article for Rs 75 and gains as much per cent as the cost price of the article in ruppes. The cost price of the article is:

a) Rs 37.50 b) Rs 40 c) Rs 50 d) RS 150

Q19. A man had 100 kgs of sugar part of which he sold at 7% profit and rest at 17% profit. He gained 10% on the whole. How much did he sell at 7% profit?

a) 65 kg b) 35 kg c) 30 kg d) 70 kg

Q20. A person bought some articles at the rate of 5 per rupee and the same number at the rate of 4 per rupee. He mixed both the types and sold at the rate of 9 for 2 rupees. In this business he suffered a loss of rs 3. The total number of articles bought by him was:

a) 1090 b) 1080 c) 540 d) 545

Q21. A shopkeep gains 20% while buying the goods and 30% while selling them. Find his total gain percent.

a) 505 b) 36% c) 56% d) 40%

Q22. The percentage of loss when an article is sold atrs50 is the as that of the profit when it is sold at Rs 70. Theabove mentionedpertangeof profit or loss on the article is

a) 10% b) 50/3% c) 20% d) 68/3

Profit andLoss :Answer Key

1 a 2 a 3 b 4 c 5 d 6 a 7 d 8 c 9 a 10 b 11 a 12 a 13 d 14 d 15 d 16 b 17 c 18 c 19 d 20 b 21 c 22 b