IPMAT Indore 2025 · Quantitative Ability · Question 32

Step 1 — work in “pool lengths”. Let the pool be 1 length long.

\text{Ankit’s speed}=\frac{1}{10}, \text{Bipul’s speed}=\frac{1}{15}\text{(lengths per minute)}

Step 2 — the combined-distance idea. Because they start at opposite ends:

they meet for the first time when their combined distance is 1 length

after that, every subsequent meeting needs a further 2 lengths of combined distance

So meetings happen when the combined distance equals 1,3,5,7,\ldots (odd numbers).

Step 3 — total combined distance in 80 minutes.

\left( \frac{1}{10}+\frac{1}{15}\right)\times 80=\frac{1}{6}\times 80=\frac{40}{3}\approx 13.33\text{lengths}

Step 4 — count the odd numbers up to 13.33.

1, 3, 5, 7, 9, 11, 13 \to 7\text{meetings}

(The next would need 15 lengths, which they do not reach.)

The graph below plots each swimmer’s position against time; every crossing of the two lines is a meeting.

Answer: Option 1 — 7