# PROFIT & LOSS (Quantitative Aptitude)

Profit and loss is an important topic for all competitive exams. From profit and loss at least two problems are asked in all bank exams like clerk, PO for SBI and IBPS. This profit and loss section will teach common formulas to solve profit & loss questions. Some important and repeated questions are covered this chapter.

## Important Formulas for Profit & Loss:

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 purchased, is called its cost price, abbreviated as C.P.
Profit or Gain : The price at which an article is purchased, is called its cost price, abbreviated as C.P.
Loss : If S.Pis less than C.P., the seller is said to have incurred a loss.

``` 1. Gain = (S.P.) - (C.P.)
2. Loss or gain is always reckoned on C.P.
3. gain% = [Gain*100/C.P.]
4. Loss = (C.P.) - (S.P.)
5. Loss% = [Loss*100/C.P.]
6. S.P. = (100+Gain%)/100 * C.P.
7. S.P. = (100-Loss%)/100 * C.P.
8. C.P. = 100/(100+Gain%) * S.P.
9. C.P. = 100/(100-Loss%) * S.P.
10. If an article is sold at a gain of say, 35%, then S.P. = 135% of C.P.
11. If an article is sold at a loss of say, 35%, then S.P. = 65% of C.P.```

### Profit & Loss: Problems with Explanations

The below profit and loss questions are common for all competitive exams. The Profit and loss is an important chapter for bank, SSC, Insurance and other state government exams. This is an easy chapter to learn and get full marks.

Before go through the problems of profit and loss. Please understand and learn basic formulas of profit and loss.

Please note question complexity is differ for each exams. While learning solve high difficulty questions to boost your knowledge. All the best.

1) A loss of 20% is made by selling an article. Had it been sold for Rs 240 more, there would have been a profit of 10%. What would be the selling price of the article if it is sold at 25% profit?
A) Rs 950
B) Rs 1020
C) Rs 975
D) Rs 1000
E) Rs 1075

Solution:
Loss = 20% = 1/5 (loss = 1, CP = 5)
CP – Loss = SP
5 – 1 = 4……….(1)
Profit% = 10% = 1/10 (Profit = 1, CP = Rs 10)
CP + P = SP
10 + 1 = 11 …….(2)
Make CP same in both equations (1) and (2) by multiplying (1) by 2. SO
10   –  2 =  8
And 10 + 1 = 11
So first, SP was 8, now is 11
So (11-8)    ->    240
3     ->      240
So 10 (CP)    ->    240/3  * 10 = 800
So after 25% profit SP   ->  1000

2) A trader sold his goods at 20% profit and along with this he used weights of 800 gm instead of 1 kg. Find his total profit%.
A) 40%
B) 45%
C) 50%
D) 55%
E) 60%

Solution:
Profit is 20%. So
1000 gm + 20% of 1000 gm = 1200 gm
so CP of 1200 gm = SP of 800 gm
Sp profit% = (1200-800)/800 * 100 = 50%

3) A shopkeeper sold his articles at cost price. But he used false weights and gives 800 gm instead of 1 kg. Find his profit%.
A) 16 2/3%
B) 20%
C) 10%
D) 33 1/3%
E) None of these

Solution:
CP of 1000 gm = SP of 800 gm
So gain% = (1000-800)/800 * 100 = 25%

4) A man bought some toffees at the rate of 3 toffees per Re. and same number at the rate of 2 toffees per Re. He mixes them and sold 3 toffees for Rs 2. Find his profit/loss% in the whole transaction.
A) 20% loss
B) 20% profit
C) 60% loss
D) 60% profit
E) None of these

Solution:
Case 1: 3 toffees per Re so 6 toffees for Rs 2
Case 2: 2 toffees per Re so 6 toffees for Rs 3
Total CP of 12 toffees = 2+3 = 5
Now he sold at 3 for Rs 2. So 12 toffees for Rs 8
Now CP = Rs 5, SP = Rs 8, so profit% = 3/5 * 100 = 60% profit

5) After selling an article at some price, a trader gain 20% on the selling price. Find his profit% on the cost price.
A) 50%
B) 33 1/3%
C) 16 2/3%
D) 25%
E) 15 1/5%

Solution:

Profit = 20% on SP
20% = 1/5, (1 – profit, 5 – SP)
CP = SP – Profit
4 = 5 – 1
so profit% on CP = profit/CP *100 = 1/4 * 100 = 25%

6) There is a profit of 20% on an article, when a discount of 10% is given. What will be the profit % on the article if discount given is 20%?
A) 2 1/3%
B) 7%
C) 4 4/5%
D) 8%
E) 6 2/3%

Solution:

P2% = (100+p%1) [ (100 – d2%)/(100 – d1%)] – 100
So P2% = (100+20) [ (100 – 20)/(100 – 10)] – 100 = 120 * (80/90) – 100 = 6 2/3%

7) A trader bought 8 kg of rice at Rs 10 per kg. While selling he uses false weights of 1600 gm instead of 2 kg. What profit did he make by selling 8 kg of rice bought?
A) Rs 18
B) Rs 30
C) Rs 20
D) Rs 26
E) Rs 33

Solution:

He uses 1600 grams weight instead of 2 kg, means he makes a profit here.
That profit% = (2000-1600)/1600 * 100 = 25%
1 kg or 1000 gm costed him Rs 10. So 1600 gms costs his Rs 16.
Now on selling each 1600 gms he makes 25% profit. So profit = 25/100 * 16 = Rs 4
On selling each 1600 gms, he makes a profit of Rs 4, so on selling 5 * 1600 = 8000 gms or 8 kg, he makes a profit of 5 * 4 = Rs 20

8) A trader gets a profit of 30% on buying a kg of wheat. By mistake, he sold 1200 grams of wheat at the price of 1 kg. Find his net profit/loss%.
A) 25/3% profit
B) 55/3% profit
C) 30/11% loss
D) 125/3% loss
E) 25/6% profit

Solution:

He sold 1200 grams of wheat at the price of 1 kg, means he incurs a loss here.
That loss% = (1200-1000)/1200 * 100 = 50/3%
Now there was a profit of 30% while buying and now a loss of 50/3% while selling. So successive method can be used here:
Profit/loss% = 30 + (-50/3) + (30)(-50/3)/100 = + 25/3%

9) A profit of 20% is made when an article is sold for Rs 720. What will be the profit % if the same article is sold for Rs 630?
A) 12%
B) 9%
C) 3%
D) 5%
E) 8%

Solution:

Let x% is the required profit. So
630 = [(100+x)/100] * [100/120 * 720] Solving, we get, x = 5% profit

10) A loss of 10% is made by selling an article. Had it been sold for Rs 75 more, there would have been a profit of 5%. What would be the selling price of the article if it is sold at 15% profit?
A) Rs 475
B) Rs 520
C) Rs 575
D) Rs 425
E) None of these

Solution:
Use shortcut for these type of questions:
CP of article = 75 × 100/ [5 – (-10)] (+5 for 5% profit, -10 for 10% loss)
So SP at 15% profit = 115/100 * CP = (115/100) * [75 × 100/15] = Rs 575