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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

Explanation:

Let the initial salaries of A, B and C be 5x, 6x and 7x respectively.

Salary of A increases by 20% and then by 40%.
∴ Salary of A after 2 years = 5x × 1.2 × 1.4 = 8.4x

Salary of C increases by 20% and then by 25%.
∴ Salary of C after 2 years = 7x × 1.2 × 1.25 = 10.5x

At the end of 2 years, B's salary is average of all three, hence B's salary will also be average of salaries of A and C.
⇒ Salary of B after 2 years = (8.4x + 10.5x)/2 = 9.45

Let the % increase in B's salary be P% in 2^nd year. Increase in first year is 25%.
⇒ 9.45x = 6x × 1.25 × (1 + P/100)
⇒ (1 + P/100) = 9.45/7.5 = 1.26
⇒ P = 26%

Hence, option (a).

Concept: Percentage Change

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