Question

Hari’s income is \[25\% \] more than Madhu’s income. Madhu’s income is less than Hari’s income by:
A. \[15\% \]
B. \[20\% \]
C. \[25\% \]
D. \[30\% \]

Answer 1

Hint: At first we will assume the income of the Madhu and from the income of Madhu we’ll find the income of Hari as Hari’s income is \[25\% \] more than Madhu’s income.
Now we’ll find the percentage that the Madhu’s income is less than Hari’s income simply by dividing the difference of income by Hari’s income multiplied by 100, simplifying this we’ll get the required percentage.

Complete step-by-step answer:
Given data: Hari’s income is \[25\% \] more than Madhu’s income
Let the income of Madhu is x
Now, \[25\% \] of Madhu’s income \[ = \dfrac{{25}}{{100}}\,\,of\,x\]
i.e. \[ = \dfrac{{25}}{{100}}\,\, \times \,x\]
On simplification we get,
 \[ = \dfrac{x}{4}\]
Now, it is given that Hari’s income is \[25\% \] more than the Madhu’s income,
i.e. Hari’s income \[ = x + \dfrac{x}{4}\]
 \[ = \dfrac{{5x}}{4}\]
Now, the percentage that Madhu’s income is less than Hari’s income $ = \dfrac{{hari'\operatorname{s} \,\,income - madhu's\,\,income}}{{hari's\,\,income}} \times 100$
On substituting the values we get,
 $ = \dfrac{{\dfrac{{5x}}{4} - x}}{{\dfrac{{5x}}{4}}} \times 100$
Multiplying with 4 in the numerator and the denominator, we get
 $ = \dfrac{{5x - 4x}}{{5x}} \times 100$
On simplification we get,
 $ = \dfrac{x}{{5x}} \times 100$
On canceling common terms we get,
 $ = 1 \times 20$
 $ = 20$
Therefore the required percentage that the Madhu’s income is less than Hari’s income is \[20\% \]
Option(B) is correct.


Note: While finding the percentage most of the students take the denominator as the Madhu’s income which is not correct solution as we have asked the percentage of Madhu’s income is less than Hari’s income, we can see in this sentence that reference has been taken of the Hari’s income so Hari’s income should be in the denominator, so try to avoid mistakes like this.