CAT 2021Slot 1QAQuestion & Solution
Question
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
Options
3:2
11:7
11:3
7:3
Solution
1. Concept Used
- Topic: Ratio and Proportion — Setting up and solving a system of linear equations from word-based conditions
- Formula: $$ \text{If } A + B = k \cdot C, \text{ eliminate variables by substitution or subtraction to find individual ratios} $$
2. Calculation
Let the daily earnings of Neeta, Geeta, and Sita be (n), (g), and (s) respectively.
From the first condition — "Neeta and Geeta together in a day = Sita alone in 6 days": $$ n + g = 6s \quad \text{...(i)} $$
From the second condition — "Sita and Neeta together in a day = Geeta alone in 2 days": $$ s + n = 2g \quad \text{...(ii)} $$
Subtract equation (i) from equation (ii): $$ (s + n) - (n + g) = 2g - 6s $$ $$ s - g = 2g - 6s $$ $$ s + 6s = 2g + g $$ $$ 7s = 3g $$
Let (g = 7a), so (s = 3a).
Substitute back into equation (i) to find (n): $$ n = 6s - g = 6(3a) - 7a = 18a - 7a = 11a $$
So the daily earnings are: $$ n = 11a, \quad g = 7a, \quad s = 3a $$
Clearly, Neeta earns the most ((11a)) and Sita earns the least ((3a)).
Required ratio: $$ n : s = 11a : 3a = 11 : 3 $$
3. Solution
Answer = Option C (11:3) ✅
The ratio of the highest daily earner (Neeta) to the lowest daily earner (Sita) is 11 : 3.