CAT 2023 Slot 1 QA Question & Solution
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
Options
Solution
Given that the salaries of Sita, Gita, and Mita are initially in the ratio $5 : 6 : 7$, let their salaries be $5p$, $6p$, and $7p$, respectively.
They receive salary hikes of 20%, 25%, and 20%, respectively.
So, their new salaries are:
$$
\frac{6}{5} \times 5p, \quad \frac{5}{4} \times 6p, \quad \frac{6}{5} \times 7p = 6p, \quad 7.5p, \quad 8.4p
$$
Now, Sita and Mita receive additional salary hikes of 40% and 25%, respectively:
Sita’s new salary is:
$$
1.4 \times 6p = 8.4p
$$
Mita’s new salary is:
$$
1.25 \times 8.4p = 10.5p
$$
Let Gita’s salary after the hike be $g$.
From the equation for the total salary:
$$
3g = 8.4p + g + 10.5p
$$
Simplifying:
$$
2g = 18.9p \implies g = 9.45p
$$
Finally, the percentage hike in Gita's salary is:
$$
\frac{9.45p - 7.5p}{7.5p} \times 100 = 26%
$$
Therefore, the percentage hike in Gita’s salary is 26%.