Question

Shikha’s income is 60% more than that of Shalu. By what percent is Shalu’s income less than Shikha’s?

Answer 1

Hint: To solve this question, we will first assume a variable for Shalu’s income and then try to determine the income of Shikha in terms of the same variable as assumed above. Then finally, we will calculate the decrease in Shalu’s income using the formula \[\dfrac{\text{Shalu }\!\!'\!\!\text{ s income}-\text{Shikha }\!\!'\!\!\text{ s income}}{\text{Shikha }\!\!'\!\!\text{ s income}}\times 100.\]

Complete step-by-step solution:
We are given in the question that Shikha’s income is 60% more than that of Shalu. First of all, let us assume a variable for Shalu’s income. Let Shalu’s income be x. Then according to the given condition in the question, as Shikha’s income is 60% more than Shalu, so we can write
Shalu’s income = x + 60 % of x
\[\Rightarrow \text{Shikha }\!\!'\!\!\text{ s income}=x+\dfrac{60}{100}x\]
\[\Rightarrow \text{Shikha }\!\!'\!\!\text{ s income}=x+0.6x\]
\[\Rightarrow \text{Shikha }\!\!'\!\!\text{ s income}=\dfrac{8}{5}x\]
So, Shikha’s income is \[\dfrac{8}{5}x.\]
Now finally we have to calculate the percent by which Shalu’s income is less than that of Shikha. That can be calculated using the formula \[\dfrac{\text{Shalu }\!\!'\!\!\text{ s income}-\text{Shikha }\!\!'\!\!\text{ s income}}{\text{Shikha }\!\!'\!\!\text{ s income}}\times 100.\]
Substituting the value of Shalu’s income and Shikha’s income in terms of the variable x, we have,
\[=\dfrac{x-\dfrac{8}{5}x}{\dfrac{8}{5}x}\times 100\]
\[=\dfrac{\dfrac{\left( 5-8 \right)}{5}x}{\dfrac{8}{5}x}\times 100\]
\[=\dfrac{\left( 5-8 \right)x}{8x}\times 100\]
= – 37.5 %
Hence, we have obtained that Shalu’s income is less than Shikha’s income by 37.5%.

Note: Students should not get confused while obtaining a minus or negative value at the answer end. We have obtained – 37.5% as there is a significant decrease in Shalu’s income than that of Shikha’s income. We can also obtain the answer by using the formula \[\dfrac{\text{Shalu }\!\!'\!\!\text{ s income}-\text{Shikha }\!\!'\!\!\text{ s income}}{\text{Shikha }\!\!'\!\!\text{ s income}}\times 100.\] But – 37.5 % is correct as it shows a decrease in amount.