Consider this problem – “A person sells x eggs and gains the selling price of y eggs. What is his profit percentage?”.
This is a typical example problem on profit and loss. When an item is sold or bought, either a profit is gained or a loss is incurred. In profit and loss problems we deal with the cost price, selling price, percentages, gain, loss etc. The aim of this section is to help you solve problems of this kind. In addition to this, you will also learn to solve problems on faulty balances.
The first lesson in this topic is a brief introduction to profit and loss. We shared some formulae that will be required to tackle problems on profit and loss. The exercises contain solved question and answers on profit, loss and faulty balances. When solving exercises, we recommend you to try solving the problems on your own, that way you will understand better and you can define your own approach to solving problems on Profit and Loss.
Introduction to Profit and Loss
Cost Price (CP)
It is the price at which an article is purchased.
Selling Price (SP)
It is the price at which an article is sold.
Profit / Loss:
It is the difference between the selling price and the cost price. If the SP is greater than CP, it is Profit; and if SP is less than CP, it is Loss.
Profit = S.P – C.P
Loss = C.P – S.P
Profit%:
It is the profit computed as a percentage of CP.
Profit% = $\frac{\text{Profit}}{\text{CP}}$ x 100
CP, Profit and Loss can also be expressed in terms of
CP (1 + profit%) = SP, if there is an overall profit in the transaction
Loss%:
It is the loss computed as a percentage of CP.
Loss% = $\frac{\text{Loss}}{\text{CP}}$ x 100
CP, Profit and Loss can also be expressed in terms of
CP( 1 – loss%) = SP, if there is an overall loss in the transaction
Note:
- Loss or gain is always based on CP.
- If a person sells two articles at the same price one at a profit of X% and the other at a loss of X%, then the seller incurs a loss given by
Loss% = $\frac{X^2}{100}$
- If a person sells goods at CP but uses false weight, the profit percentage of the person is given by
Profit% = $\frac{\text{True Weight – False Weight}}{\text{False Weight}}$ x 100
Problems
Profit and Loss - Exercise - Blog
14 questions
- Rashmi buys 5 kgs of mangoes for Rs.110 and sells them at the rate of Rs. 20 per kg. Find her profit / loss%.
- 9.09%
- 11.11%
- 18.18%
- 22.22%
Show the answer
Answer: 9.09%
Cost price of 1kg of mango = $\frac{110}{5}$ = 22
Since Rashmi sells Rs. 22/kg mango at Rs. 20/kg, she incurs a loss. The percentage loss is given by $\frac{22 - 20}{22}$ x 100 = 9.09 %
- Mohit gains 20% on selling an article for Rs. 1200. Find the CP of the article.
- Rs. 900
- Rs. 950
- Rs. 1000
- Rs. 1050
Show the answer
Answer: Rs. 1000
Let the CP of the article be $x$. Then,
20% = $\frac{1200 - x}{x}$
$\frac15 = \frac{1200-x}{x}$
6$x$ = 6000
$x$ = 1000.
Therefore, the cost price of the article is Rs. 1000
- Ashish buys 6 chocolates for Rs.1 and sells it at the rate of 5 chocolates for Rs. 1. Find his profit / loss%.
- 15%
- 20%
- 25%
- 30%
Show the answer
Answer: 20%
Cost price of 1 chocolate = Rs. $\frac16$
Selling price of 1 chocolate = Rs. $\frac15$
Profit% = $\frac{\frac15 - \frac15}{\frac16}$ x 100%
= 20%
Ashish gains a percentage of 20.
- Shiva sells an article for Rs. 2000, at a loss of 20%. At what price must he sell the article to gain 12%?
- Rs. 2400
- Rs. 2650
- Rs. 2800
- Rs. 3000
Show the answer
Answer: Rs. 2800
Let the cost price of the article be $x$.
$x$ x (1 - loss%) = SP
Then $x$ x (1 - $\frac{20}{100}$) = 2000
$x$ = 2500.
The cost price of the article is Rs. 2500. To gain a profit of 12%, Shiva must sell at
2500 x (1 + $\frac{12}{100}$) = Rs. 2800
- Abhinav buys 6 chocolates for Rs. 5. If he wants to sell the chocolates at a profit of 20%. What must be the SP of the chocolates.
- R.s 5.5
- Rs. 6
- Rs. 6.5
- Rs. 7
Show the answer
Answer: Rs. 6
The cost price of one chocolate is Rs. $\frac56$
A profit of 20% on each chocolate is given by
$\frac56$ x (1+$\frac{20}{100}$) = Rs. 1
In order to gain 20%, Abhinav must sell 6 chocolates at 6 x 1 = Rs. 6
- CP of 20 chocolates is equal to SP of 15 chocolates. Find the profit/loss%
- 25%
- 33.33%
- 28.28%
- 30%
Show the answer
Answer: 33.33%
Let the CP of one chocolate be $x$. Then,
SP of 15 chocolates = CP of 20 chocolates = 20$x$.
CP of 15 chocolates = 15$x$.
Profit% = $\frac{20x - 15x}{15x}$ x 100 = 33.33%
- A person sells 70 eggs and gains the selling price of 14 eggs. Find his profit%
- 20%
- 25%
- 30%
- 35%
Show the answer
Answer: 25%
Let the CP of each egg be $x$. Then,
SP of 70 eggs - CP of 70 eggs = SP of 14 eggs.
SP of 56 eggs = CP of 70 eggs = 70x
CP of 56 eggs = 56$x$
Profit% = $\frac{70x - 56x}{56x}$ x 100 = 25%
- If a person loses a CP of 5 mangoes on selling 25 mangoes. Find his loss%
- 20%
- 15%
- 14.14%
- 28.28%
Show the answer
Answer: 20%
Let CP of each mango be $x$.
Since the person is incurring a loss of CP of 5 mangoes,
CP of 25 mangoes - SP of 25 mangoes = CP of 5 mangoes.
CP of 20 mangoes = SP of 25 mangoes = 20x
CP of 25 mangoes = 25$x$
loss % = $\frac{25x - 20x}{25x}$ x 100 = 20%
- A dishonest dealer professes to sell his goods at CP but uses a faulty weight of 1kg and gains 10%. Find the weight used by the dealer.
- 1111.1gm
- 909.09gm
- 900gm
- 1100gm
Show the answer
Answer: 909.09gm
Let weight of the item sold by the dealer be $x$ gms, instead of 1 kg. Then,
10 = $\frac{1000 - x}{x}$ x 100
$x$ = 909.09 gm
- Ajith buys two cycles for Rs. 1200 and sells one at a profit of 10% and the other at a loss of 10%. Find the net profit or loss incurred by Ajith.
- No profit or loss
- 5% profit
- 5% loss
- 10% profit
Show the answer
Answer: No profit or loss
Selling price of the cycle with a profit of 10% = 1200 (1 + $\frac{10}{100}$) = Rs. 1320
Selling price of the cycle with a loss of 10% = 1200 (1 - $\frac{10}{100}$) = Rs. 1080
Net Selling Price of the cycles = 1320 + 1080 = 2400.
Net Cost price = 1200 x 2 = Rs. 2400.
Ajith incurs no profit or loss.
Note: There is no profit or loss incurred for the same cost price and equal profit and loss percentage.
- A person sells two article for Rs. 990 each. He gains 10% profit on one article and 10% loss on the other. Find his gain/loss%.
- 10% profit
- 10% loss
- 1% profit
- 1% loss
Show the answer
Answer: 1% loss
Let the cost price of the article with a profit of 10% be $x$, then
$x$ (1 + $\frac{10}{100}$) = 990 => $x$ = 900
Let the cost price of the article with a loss of 10% be $y$, then
$y$ (1 - $\frac{10}{100}$) = 990 => $y$ = 1100
Net Selling Price of the articles = 990x2 = Rs. 1980.
Net Cost price = 900 + 1100 = Rs. 2000.
Loss% = 2000 - 1980 / 2000 = 1%
Note : If a person sells two articles at the same price one at a profit of X% and the other at a loss of X%, then the seller incurs a loss given by
Loss% = $\frac{X^2}{100}$
- Ravi sells one article for Rs. 672 at a profit of 12% and sells another article for Rs. 425 at a loss of 15%. Find Ravi’s overall gain/loss%.
- 2.5% profit
- 2.5% loss
- 3% profit
- 3% loss
Show the answer
Answer: 2.5% profit
Let the cost price of the article with a profit of 12% be $x$, then
$x$ (1 + $\frac{12}{100}$) = 672 => $x$ = 600
Let the cost price of the article with a loss of 10% be y, then
$y$ (1 - $\frac{20}{100}$) = 400 => $y$ = 500
Net Selling Price of the articles = 672+425 = Rs. 1072.
Net CP = 600 + 500 = Rs. 1100.
Loss % = $\frac{1100 - 1097}{1100}$ x 100 = 2.54%
- A sells an AC to B at a loss of 30%. B sells it to C at a profit of 10%. C repairs the AC for Rs. 160 and sells it to D at a profit of 12% for Rs.1120. Find the price at which the article was sold to B.
- Rs. 800
- Rs. 900
- Rs. 1000
- Rs. 1120
Show the answer
Answer: Rs. 1000
Let the cost price at which A buys the AC be $x$. Then,
The price at which A sells it to B = $x$ (1 - $\frac{30}{100}$)= .7$x$
B sells the AC to C at a profit of 20% = .7$x$ (1+$\frac{2}{100}$) = .84$x$
C repairs the AC for Rs. 160. So, total amount spent by C on AC = .84$x$ + 160
C then sells the AC to D at a profit of 12% = (.77$x$ + 160) x (1+$\frac{12}{100}$)
(.84$x$+160) x 1.12 = 1120
.84$x$ + 160 = 1000
$x$ = 1000
The article was bought by A at Rs. 1000
- Out of 150 pens, Mr. A sells x pens at a profit of 20% and sells the remaining pens at a loss of 10%. If Mr. A gets an overall profit of 15%. Find the number of pens sold at a profit of 20%.
- 70
- 90
- 110
- 130
Show the answer
Answer: 130
Let the CP of each pen be Rs.1
$x$ pens are sold at a profit of 20% => $x$ (1+$\frac{20}{100}$)
150-$x$ pens are sold at a loss of 10% => (150-$x$) (1-$\frac{10}{100}$)
Overall profit = 150 x (1+$\frac{16}{100}$) = 174
$x$(1 + ${20}{100}$) + (150-$x$) (1-$\frac{10}{100}$) = 174
1.2$x$ + .9(150-$x$) = 174
$x$ = 130
The number of pens sold at a profit of 20% = 130.
