Averages , Ratio and Proportion Question 2 - CAT 2021
The amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days. The amount Sita and Neeta together earn in a day equals what Geeta alone earns in 2 days. The ratio of the daily earnings of the one who earns the most to that of the one who earns the least is:
Step-by-Step Explanation
Let the daily earnings of Neeta, Geeta, and Sita be n, g, and s, respectively.
- Set up the linear systems:
n + g = 6s --- (Equation 1)
s + n = 2g
Therefore:
n = 2g − s --- (Equation 2)
- Solve for relative components:
Substitute Equation 2 into Equation 1:
2g − s + g = 6s
3g = 7s
g/s = 7/3
Let us assume a common scalar value:
s = 3k and g = 7k.
Substitute these values back into Equation 2 to isolate n:
n = 2(7k) − 3k = 14k − 3k = 11k
- Determine the final target ratio:
Comparing the parameters (n = 11k, g = 7k, s = 3k), Neeta is the highest earner and Sita is the lowest earner.
Ratio = 11k : 3k
= 11 : 3
Correct Option: C