Question

The salaries of three friends Sita, Gita and Mita are initially in the ratio 5: 6: 7 , respectively. In the first year, they get salary hikes of 20%, 25% and 20% , respectively. In the second year, Sita and Mita get salary hikes of 40% and 25% , respectively, and the salary of Gita becomes equal to the mean salary of the three friends. The salary hike of Gita in the second year is

• A. 27%
• B. 24%
• C. 26%
• D. 28%

Answer 1

The Correct Option is C

Let the initial salaries of Sita, Gita, and Mita be: 

• Sita: \( 5p \)
• Gita: \( 6p \)
• Mita: \( 7p \)

They receive hikes as follows:

• Sita: 20% hike ⇒ New salary = \( 5p \times \frac{6}{5} = 6p \)
• Gita: 25% hike ⇒ New salary = \( 6p \times \frac{5}{4} = 7.5p \)
• Mita: 20% hike ⇒ New salary = \( 7p \times \frac{6}{5} = 8.4p \)

Now, Sita and Mita get another hike:

• Sita: 40% hike ⇒ New salary = \( 6p \times 1.4 = 8.4p \)
• Mita: 25% hike ⇒ New salary = \( 8.4p \times 1.25 = 10.5p \)

Let Gita's new salary after this round of hike be \( g \).

We are told that the new average salary of all three = average of updated salaries =

\[ \frac{8.4p + g + 10.5p}{3} = g \]

Multiply both sides by 3:

\[ 8.4p + g + 10.5p = 3g \] \[ 18.9p + g = 3g \Rightarrow 2g = 18.9p \Rightarrow g = \frac{18.9p}{2} = 9.45p \]

So, Gita’s new salary is \( 9.45p \).

Gita’s old salary after first hike was \( 7.5p \). Now it is \( 9.45p \).

Hence, the percentage increase in Gita’s salary is:

\[ \frac{9.45p - 7.5p}{7.5p} \times 100 = \frac{1.95p}{7.5p} \times 100 = 26\% \]

Final Answer: 26% (Option C)