CAT 2023 Slot 1 · Quant · Question 12

Take the starting salaries as 5, 6 and 7 units for Sita, Gita and Mita.

After the first year's hikes, Sita has 5\times 1.2=6.

Gita has 6\times 1.25=7.5.

Mita has 7\times 1.2=8.4.

In the second year Sita rises by 40% to 6\times 1.4=8.4.

Mita rises by 25% to 8.4\times 1.25=10.5.

Let Gita's second-year salary be G; it is stated to equal the mean of all three.

So G=\frac{8.4+G+10.5}{3}, which gives 3G=18.9+G.

Therefore 2G=18.9 and G=9.45.

Gita's salary rose from 7.5 to 9.45, an increase of 9.45-7.5=1.95.

As a percentage, \frac{1.95}{7.5}=0.26, that is 26% — the first option.

Shortcut. When one value equals the mean of three, it also equals the mean of the other two. So Gita's new salary is simply \frac{8.4+10.5}{2}=9.45, with no equation to solve at all.