# Profit and Loss Questions

FACTS  AND  FORMULAE  FOR  PROFIT  AND  LOSS  QUESTIONS

Selling Price (SP) : The price at which the shopkeeper sells the goods is called the selling price (SP) of the goods sold by the shopkeeper.

Profit : If the selling price of an article is more than its cost price, then the dealer (or shopkeeper) makes a profit (or gain)

i.e Profit = SP - CP;       SP > CP

Loss : If the selling price of an article is less than its cost price, then the dealer suffers a loss.

i.e loss = CP - SP;        CP > SP

IMPORTANT FORMULAE

1. Profit percentage = $\inline \fn_cm \frac{Profit}{Cost \; Price}\times 100$

2. Loss percentage = $\inline \fn_cm \frac{Loss}{Cost \; Price}\times 100$

3. $\inline \fn_cm SP =\left [ \frac{(100+Gain \; percentage)}{100} \times CP \right ]=\left [ \frac{(100-Loss \; percentage)}{100} \times CP \right ]$

4. $\inline \fn_cm CP =\left [ \frac{100}{(100+Gain \; percentage)} \times SP \right ]=\left [ \frac{100}{(100-Loss \; percentage)} \times SP \right ]$

5. If an article is sold at a gain of say 35%, then SP = 135% of CP

6. If an article is sold at a loss of say 35%, then SP = 65% of CP

7. When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss given by :$\inline \fn_cm Loss\; Percentage=\left ( \frac{Common\; Loss\; and\; Gain\; percentage}{10} \right )^2=\left ( \frac{x}{10} \right )^2$

8. If a trader Professes to sell his goods at cost price, but uses false weihts, then

$\inline \fn_cm Gain\; Percentage=\left [ \frac{Error}{(True\: value)-(Error)}\times 100 \right ]$%

Q:

A milkman purchases the milk at Rs. x per litre and sells it at Rs. 2x per litre still he mixes 2 litres water with every 6 litres of pure milk. What is the profit percentage?

 A) 116% B) 166.66% C) 60% D) 100%

Explanation:

Let the cost price of 1 litre pure milk be Re.1, then

$\inline&space;\begin{Bmatrix}&space;6&space;&&space;litres(milk)&space;&&space;\rightarrow&space;&&space;CP=Rs.6\\&space;2&space;&&space;litres(water)&space;&&space;\rightarrow&space;&&space;CP=Rs.0&space;\end{Bmatrix}\rightarrow&space;CP=Rs.6&space;only$

and 8 litre mixture  $\rightarrow$ SP $\rightarrow$ 8 x 2 = Rs.16

Profit %= $\inline \left [ \frac{\left ( 16-6 \right )}{6} \right ]\times 100=\frac{1000}{6}=166.66$%

140 19885
Q:

A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:

 A) No profit, no loss B) 5% C) 8% D) 10%

Explanation:

C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.

S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.

Gain =${\color{Black}&space;\left&space;(&space;\frac{80}{1600}&space;\times&space;100\right&space;)&space;}$% = 5%

129 18827
Q:

By selling 45 lemons for Rs 40, a man loses 20 %. How many should he sell for Rs 24 to gain 20 % in the transaction ?

 A) 16 B) 18 C) 20 D) 22

Explanation:

Let S.P. of 45 lemons be Rs. x.

Then, 80 : 40 = 120 : x or   x = $\inline \frac{40\times 120}{80}$= 60

For Rs.60, lemons sold = 45

For Rs.24, lemons sold  =$\inline \frac{45}{60}\times 24$= 18.

144 18512
Q:

A shopkeeper cheats to the extent of 10% while buying and selling, by using false weights. His total gain is.

 A) 20% B) 21% C) 22% D) 23%

Explanation:

Gain % = $\inline&space;\fn_jvn&space;{\color{Black}&space;(\frac{(100+common\;&space;gain\;&space;percent)^{2}}{100}-100)}$%

= $\inline&space;\fn_jvn&space;{\color{Black}&space;(\frac{(100+10)^{2}}{100}-100)}$%

= $\inline&space;\fn_jvn&space;{\color{Black}&space;(\frac{12100-10000}{100})}$%

= 21%

80 14995
Q:

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:

 A) 15 B) 16 C) 18 D) 25

Explanation:

Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.

S.P. of x articles = Rs. 20.

Profit = Rs. (20 - x).

${\color{Black}&space;\therefore&space;\left&space;(&space;\frac{20-x}{x}\times&space;100=25&space;\right&space;)}$

$\inline \fn_jvn \Rightarrow$2000 - 100x = 25x

$\inline \fn_jvn \Rightarrow$125x=2000

$\inline \fn_jvn \Rightarrow$x=16