QuestionIf Ram earns 20% more than Hari, what percent less is Hari's income than Ram's? Options: (a) 16 2/3% (b) 20% (c) 23 1/3% (d) 17% (e) None.

Studdy Solution

STEP 1

Assumptions1. Ram's income is20% more than Hari's income. . We need to find the percentage of Hari's income which is less than Ram's income.

STEP 2

Let's assume Hari's income as $x$ . According to the problem, Ram's income is20% more than Hari's. So, we can write Ram's income as $x +20\% \, of \, x$ .
$Ram's\, income = x +0.20x$

STEP 3

implify the above expression to find Ram's income in terms of x.
$Ram's\, income =1.20x$

STEP 4

Now, we need to find the percentage of Hari's income which is less than Ram's. This is the same as finding the percentage decrease from Ram's income to Hari's income. The formula for percentage decrease is $Percentage\, decrease = \frac{{Initial\, value - Final\, value}}{{Initial\, value}} \times100\%$

STEP 5

In this case, the initial value is Ram's income and the final value is Hari's income. Substituting these values into the formula gives $Percentage\, decrease = \frac{{Ram's\, income - Hari's\, income}}{{Ram's\, income}} \times100\%$

STEP 6

Substitute the expressions for Ram's income and Hari's income (which we assumed as x) into the formula $Percentage\, decrease = \frac{{1.20x - x}}{{1.20x}} \times100\%$

STEP 7

implify the above expression to find the percentage decrease $Percentage\, decrease = \frac{{0.20x}}{{1.20x}} \times100\%$

STEP 8

implify further by cancelling out the x in the numerator and the denominator $Percentage\, decrease = \frac{{0.20}}{{1.20}} \times100\%$

STEP 9

Calculate the percentage decrease $Percentage\, decrease =16.67\%$ So, Hari's income is $16.67\%$ less than Ram's income, which is approximately $16 \frac{2}{3} \%$ .
Therefore, the answer is (a) $16 \frac{2}{3} \%$ .

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