CAT 2023Slot 1QAQuestion & 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
25%
28%
26%
30%
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%.