CAT 2021 Slot 1 QA Question & 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
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.