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

Initial salaries for Sita, Gita, and Mita are:

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

Salary hikes are applied as follows:

• Sita: 20% hike results in a new salary of \( 5p \times 1.20 = 6p \)
• Gita: 25% hike results in a new salary of \( 6p \times 1.25 = 7.5p \)
• Mita: 20% hike results in a new salary of \( 7p \times 1.20 = 8.4p \)

Sita and Mita receive another hike:

• Sita: 40% hike results in a new salary of \( 6p \times 1.4 = 8.4p \)
• Mita: 25% hike results in a new salary of \( 8.4p \times 1.25 = 10.5p \)

Let Gita's salary after this second round of hikes be \( g \).

The updated average salary of all three is equal to Gita's new salary \( g \):

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

Multiplying both sides by 3:

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

Gita's new salary is \( 9.45p \).

Gita's salary after the first hike was \( 7.5p \), and her current salary is \( 9.45p \).

The percentage increase in Gita's salary is calculated as:

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

Final Answer: 26% (Option C)