## Quantitative Aptitude Notes: Profit & Loss

** ****PROFIT & LOSS Notes for IBPS, SSC and SBI PO**

**COST PRICE:** The price at which a person buys an article is called the cost price of the article. Cost price is denoted by C.P.

**SELLING PRICE :** The price at which an article is sold is called its selling price. Selling price is denoted by S.P.

**PROFIT (GAIN) :** If S.P. of an article is more than its C.P. there is a profit (gain).

Profit = S.P. – C.P.

Percentage Profit = (Profit / C.P.) * 100

**LOSS : **If S.P. of an article is less than its C.P., there is a loss.

Loss = C.P. – S.P.

Percentage loss = (loss / C.P.) * 100

Percentage profit and percentage loss are always calculated on C.P. unless otherwise stated.

**Example :** An article is bought for Rs. 300. Find its S.P. if it is sold at:

1) 10% profit 2) 20% loss

**Solution :** Profit = 10% of C.P.

= (10 / 100) * 300

= 30

S.P. = C.P. + profit

= 300 +30

= 330

Loss = 20% of C.P.

= (20 / 100) * 300

= 60

S.P. = C.P. – loss

= 300 – 60

= 240

**SHORT TRICKS**

Suppose there is a profit of P%, it means that S.P. is equal to (100+P)% of C.P. i.e.

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

If there is a loss of p% then,

S.P. = C.P. (100-p)100

**Example :** an article is sold for Rs. 480. Find its C.P. if it is sold at

1) 20% profit 2) 20% loss

**Solution : 1)** C.P. = [ S.P. * (100 / 120) ]

= 480 * (100 / 120)

= 400

** ****2)**** **C.P. = 480 * (100 / 80)

= 600

**Marked price:** when we go to the market to purchase an article, we find the price of the article printed either on the article or on a tag attached to it. This price s called marked price (M.P.) of the article. The M.P. is also called listed price or quoted price.

**Discount:** in order to dispose the old or damaged goods,some traders offer a certain percentage of the marked price of the goods as discount.

Discount is always given on the M.P.

Selling Price = M.P. – Discount

If there is a discount of d%, it means that S.P. is equal to (100-d)% of M.P.

S.P. = M.P. * [ (100-d) / 100 ]

**Overhead Charges:** The extra cost that includes transportation fees, maintenance,packaging and advertisement fees etc. are called overheads.

Overheads are always added to the C.P. to get the total C.P. and then profit % or loss % are calculated on the total C.P.

**Example:** a manufacturer marks an article for Rs. 7500 and then sells it to a trader at 20% discount. Find the percentage profit made by the trader, if he sells this article at 10% discount.

**Solution:** C.P. for trader = 7500 * (80 / 100)

= 6000

S.P. for trader = 7500 * (90 / 100)

= 6750

% profit = (750 / 6000) * 100

= 12.5%

**Successive Discounts:** In case of successive discounts, the first discounts, in order, is calculated on M.P. and is subtracted from it. The second discount is then calculated on the resulting amount is again subtracted and so on. The amount left after subtracting the last discount is selling price of the article.

When discount is d%.

S.P. = [(100-d) / 100] * M.P.

In case of two successive discounts d1% and d2%

S.P. = [(100 – d1) / 100 * (100 – d2) / 100 *M.P.]

In case of three successive discounts d1%, d2% and d3%

S.P. = [(100 – d1) / 100 * (100 – d2) / 100 ( 100 – d3) / 100 * M.P]. And so on.

**Example:** The M.P. of an article is 100 and is available at three successive discounts 20%, 15%and 10%. Find the S.P. of an article.

**Solution:** S.P. = 100 * (80 / 100) * (85 / 100) * (90 / 100)

= 61.2

**Worked-out Questions on Profit & Loss **

**An article is sold for Rs. 4600 at a gain of 15%. What would be the profit or loss percent if it is sold for Rs. 3600 ?**

**Solution:**C.P. = (100 / 115) * 4600

= 4000

If S.P. = 3600, then

loss % = (400 / 4000) * 100

= 10%

- A man sold his car at a loss of 5%. Had he sold it for Rs. 18000 more, he would have

**Solution:**Initial S.P. is at 5% loss

New S.P. is at 4% profit

The difference in the two S.P. = 9% of C.P.

9% of C.P. = 18000

C.P. = 18000 * (100 / 9)

= Rs. 200000

- By selling two articles, a man gains Rs. 3750 on the whole. He sells one article for Rs.69000 at 15% profit. Find the cost price of the other article if it is sold at 20% loss.

**Solution:**Profit = 69000 * (15 / 115)

= 9000

To gain on whole, he must have a loss of 9000 – 3750 = 5250 on the other article

20% of C.P. = 5250

C.P. = 5250 * 5

= 26250

- Two brands of tea costing Rs. 850 and Rs. 950 per kg respectively are mixed in the ratio 3:5 by weight. If one-fourth of the mixture is sold at Rs. 1100 per kg and the remaining at the rate of Rs. 1200 per kg, find the profit percent on the whole.

**Solution:**Let 3 kg of Rs. 850 per kg and 5 kg of 950 per kg be mixed together.

C.P. of the mixture = 3 * 850 + 5 * 950

= 7300

One -fourth of 8 kg = 2 kg

Remaining mixture = 6 kg

S.P. of the mixture = (2 * 1100) + (6 * 1200)

= 9400

Profit % = (2100 / 7300) * 100

= 28.77%

- 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 for it for Rs. 2 less, he would have gained 10% . find the cost price of the article.

**Solution****:**Let C.P. = 100

Then S.P. = 105

If new C.P. = 95

And new S.P. with 10% profit = 104.5

Then the difference in S.P. = .5

When the difference is 2, then C.P. = 100 * (2 / .5)

= 400

- S.P. of 20 identical pens is equal to the C.P. of 15 identical pens. Find the % profit or % loss.

**Solution**: Let S.P. of 20 pens = 100

S.P. of 15 pens = 75

C.P. of 15 pens = 100

% loss = (25 / 100) * 100

= 25%

- A man buys an article whose marked price is Rs.800 and available at two successive discounts 25% and 15%. He tagged new M.P. on the article and give 10% discount further and want to sold at a 20% profit. Find the new M.P. of the article.

**Solution:**C.P. of article for a man = 800 * (75 / 100) * (85 / 100)

= 510

S.P. of the article for a man = 510 * (120 / 100)

= 612

New M.P. = 612 * (100 / 90)

= 680

- The profit earned after selling an article for Rs. 1516 is the same as loss incurred after selling the article for Rs. 1112. What is the cost price of the article ?

**Solution:**Let profit = loss = x

1516 – x = 1112 + x

1516 – 1112 = 2x

2x = 404

x = 404/2

x = 202

C.P. = 1112 + 202

= 1314

- A man sold a wristwatch for Rs. 2400 at a loss of 25%. At what rate should he have sold the wristwatch to earn a profit of 25% ?

**Solution:**C.P. = 2400 * (100 / 75)= 3200

New S.P. = 3200 * (125 / 100)

= 4000

- What is a single discount equivalent to three successive discounts 20%,10% and 15% ?

**Solution:**Let marked price be 100

Then, S.P. = [ 100 * (80 /100) * (90 / 100) * (85 / 100) ]

= 61.2

Equivalent single discount = 100 – 61.2

= 38.8%

These Notes have been provided by Plutus Academy, one of the best SSC and IBPS coaching institute.

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