CAT 2021 Slot 3 QA Q3 Time, Speed & Distance

Question 3 of the Quantitative Ability (QA) section, CAT 2021 Slot 3, with CAT's official answer and a worked solution.

Mira and Amal walk along a circular track, starting from the same point at the same time. If they walk in the same direction, then in 45 minutes, Amal completes exactly 3 more rounds than Mira. If they walk in opposite directions, then they meet for the first time exactly after 3 minutes. The number of rounds Mira walks in one hour is

TITA: type in the answer. There are no options and no negative marking.

Answer: 8 Time, Speed & Distance TITA

Solution

Let speeds be \(a\) (Amal) and \(m\) (Mira) in rounds per minute.
Same direction: \(45(a - m) = 3 \Rightarrow a - m = \frac{1}{15}\). Opposite: \(3(a + m) = 1 \Rightarrow a + m = \frac13\).
\(m = \frac12\left(\frac13 - \frac1{15}\right) = \frac{2}{15}\) rounds per minute.
In 60 minutes Mira walks \(60 \times \frac{2}{15} = 8\) rounds.