Arithmetic

Ratio, Proportion & Variation

Easy

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

$26\%$

$25\%$

$28\%$

$30\%$

✅ Correct Option: 1

We need to track salary changes over two years and find Gita's second-year hike when her salary equals the mean of all three salaries.

Initial ratio: Sita : Gita : Mita = 5 : 6 : 7

When working with ratios, we can use any common multiplier. Let's use the ratio values directly:

Sita's initial salary = 5 units

Gita's initial salary = 6 units

Mita's initial salary = 7 units

First year hikes: 20%, 25%, and 20% respectively

To find salary after a percentage increase, multiply by (1 + percentage/100)

Sita: 5 × (1 + 20/100) = 5 × 1.20 = 6 units

Gita: 6 × (1 + 25/100) = 6 × 1.25 = 7.5 units

Mita: 7 × (1 + 20/100) = 7 × 1.20 = 8.4 units

After first year: 6 : 7.5 : 8.4

Second year hikes: Sita gets 40%, Mita gets 25%, Gita's salary = mean of all three

Sita: 6 × (1 + 40/100) = 6 × 1.40 = 8.4 units

Mita: 8.4 × (1 + 25/100) = 8.4 × 1.25 = 10.5 units

Gita: Let's call this x units (we need to find this)

After second year: 8.4 : x : 10.5

Given: Gita's salary = Mean of all three salaries

Mean = $\tfrac{\text{Sum of all values}}{\text{Number of values}}$

Mean of three salaries = $\tfrac{8.4 + x + 10.5}{3} = \tfrac{18.9 + x}{3}$

Since Gita's salary equals the mean:

$x = \tfrac{18.9 + x}{3}$

$3x = 18.9 + x$

$3x - x = 18.9$

$2x = 18.9$

$x = 9.45$

Therefore: Gita's salary after second year = 9.45 units

Gita's salary change:

Before second year: 7.5 units

After second year: 9.45 units

Increase: 9.45 - 7.5 = 1.95 units

Percentage increase = $\tfrac{\text{Increase}}{\text{Original value}} \times 100$

Percentage increase = $\tfrac{1.95}{7.5} \times 100 = \tfrac{1.95 \times 100}{7.5} = \tfrac{195}{7.5} = 26\%$

Gita's salary hike in the second year is 26%

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