Averages , Ratio and Proportion Question 4 - CAT 2023
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:
Step-by-Step Explanation
Let the initial salaries of Sita, Gita, and Mita be 50, 60, and 70 respectively (scaling by 10 to avoid decimals).
- Calculate Year 1 Salaries:
- Sita (+20%): 50 × 1.20 = 60
- Gita (+25%): 60 × 1.25 = 60 + 15 = 75
- Mita (+20%): 70 × 1.20 = 70 + 14 = 84
- Calculate Year 2 Salaries:
- Sita (+40%): 60 × 1.40 = 60 + 24 = 84
- Mita (+25%): 84 × 1.25 = 84 + 21 = 105
- Let Gita's Year 2 salary be G₂.
- Apply the Mean Salary Condition:
In Year 2, Gita's salary equals the average of all three salaries:
G₂ = (84 + G₂ + 105)/3
3G₂ = 189 + G₂
2G₂ = 189
⟹ G₂ = 94.5
- Calculate Gita's Year 2 Hike Percentage:
Gita's salary went from 75 (end of Year 1) to 94.5 (end of Year 2).
Hike = 94.5 − 75 = 19.5
Hike Percentage = 19.5/75 × 100% = 26%
Correct Option: C
💡 FundaMakers Tip:
If a person's value is equal to the average of the entire group, it simply means their value is exactly equal to the average of the other members of the group!
Skip the equation G₂ = (84 + G₂ + 105)/3 and directly write:
G₂ = (84 + 105)/2 = 189/2 = 94.5.
This logic rule works for any group size and saves you algebra steps!