Question

# Sambhu buys rice at Rs 10 per kg and puts a price tag on it, so as to earn a profit of 20 percent. However, his faulty balance shows 1000 gm when it is actually 800 gm. What is his actual gain percentage?

Hint- Here, we will proceed by using the formula Selling price = (1+$\dfrac{{{\text{Profit percent}}}}{{100}}$)(Cost price) in order to calculate the selling price of 800 gm (actual) of rice corresponding to cost price of 1000 gm of rice.

Given, Cost price of 1 kg or 1000 gm of rice, CP = Rs 10
It is also given that sambhu puts a price tag on this rice so as to earn a profit of 20 percent.
Profit percentage = 20 percent
It is also given that Sambhu’s faulty balance shows 800 gm as 1000 gm. So, the selling price for 1000 gm which he will be tagging is actually the selling price for 800 gm.
As we know that Selling price = (1+$\dfrac{{{\text{Profit percent}}}}{{100}}$)(Cost price) i.e., SP= (1+$\dfrac{{{\text{Profit percent}}}}{{100}}$)(CP)
Using the above formula, we get
Selling price of 800 gm of rice = (1+$\dfrac{{{\text{Profit percent}}}}{{100}}$)(Cost price of 1000 gm of rice)
$\Rightarrow$Selling price of 800 gm of rice$= \left( {1 + \dfrac{{20}}{{100}}} \right) \times 10 = \left( {\dfrac{{100 + 20}}{{100}}} \right) \times 10 = \left( {\dfrac{{120}}{{100}}} \right) \times 10 = {\text{Rs }}12$
As the selling price of 800 gm of rice = Rs 12
$\Rightarrow$Selling price of 1 gm of rice = Rs $\dfrac{{12}}{{800}}$

$\Rightarrow$Selling price of 1000 gm of rice = $\left( {\dfrac{{12}}{{800}}} \right) \times 1000 = {\text{Rs 15}}$
Here, taking 1000 gm as the reference amount of the rice in order to calculate the actual gain (profit) and the actual gain percentage.
Actual profit or gain = SP of 1000 gm of rice – CP of 1000 gm of rice = 15-10 = Rs 5
Also we know that profit percentage or gain percentage = $\left( {\dfrac{{{\text{Actual profit or gain}}}}{{{\text{Cost price}}}}} \right) \times 100$ percent
Using the above formula, we get
Actual gain percentage = $\left( {\dfrac{{{\text{Actual gain}}}}{{{\text{Cost price of 1000 gm of rice}}}}} \right) \times 100 = \left( {\dfrac{5}{{10}}} \right) \times 100 = 50$ percent
Hence, the actual gain percentage is 50 percent.

Note- In this particular problem, when sambhu measure 800 gm (actual amount) of rice the balance will show 1000 gm (apparent amount) of rice due to which the selling price corresponding to cost price of 1000 gm of rice and 20 percent as gain percentage is actually for 800 gm of rice and we have taken 1000 gm as the reference amount to calculate gain percentage so there is a need to find the selling price corresponding to 1000 gm (actual amount).