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
Let the daily earnings of Neeta, Geeta, and Sita be $n$, $g$, and $s$ respectively.
It is given that:
$$
\text{(i) } n + g = 6s
$$
$$
\text{(ii) } s + n = 2g
$$
Subtracting (i) from (ii):
$$
(s + n) - (n + g) = 2g - 6s \implies s - g = 2g - 6s
$$
$$
\implies 7s = 3g
$$
Let $g = 7a$. Then:
$$
s = 3a
$$
Now, Neeta’s earning:
$$
n = 6s - g = 6 \times 3a - 7a = 18a - 7a = 11a
$$
Hence, the ratio of Neeta’s earning to Sita’s earning is:
$$
n : s = 11a : 3a = 11 : 3
$$
Therefore, the ratio of Neeta’s to Sita’s earnings is 11:3.