Mira and Amal walking on a circular track

CAT 2021 Slot 3 · QA · Medium · Circular races

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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

Answer

8

Explanation

Let vAv_A and vMv_M be the speeds of Amal and Mira in rounds per minute.

When walking in the same direction: 45(vA−vM)=3  ⟹  vA−vM=11545(v_A - v_M) = 3 \implies v_A - v_M = \frac{1}{15}

When walking in opposite directions, meeting time is 3 minutes: 3(vA+vM)=1  ⟹  vA+vM=133(v_A + v_M) = 1 \implies v_A + v_M = \frac{1}{3}

Subtracting the two equations: 2vM=13−115=415  ⟹  vM=215 rounds per minute2v_M = \frac{1}{3} - \frac{1}{15} = \frac{4}{15} \implies v_M = \frac{2}{15}\text{ rounds per minute}

In 60 minutes, Mira walks: 60×215=8 rounds60 \times \frac{2}{15} = 8\text{ rounds}.

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