IPMAT Indore 2024 · Quantitative Ability · Question 28

Step 1 — get the two effective speeds. Read them straight off the first sentence; you never need the boat’s own speed or the stream’s.

\text{Upstream speed}=\frac{96}{8}=12\text{km/h}, \text{Downstream speed}=\frac{96}{6}=16\text{km/h}

Step 2 — one cycle. Each cycle is 1 hour downstream then 1 hour upstream:

+16-12=+4\text{km (net displacement downstream)}

Step 3 — five cycles. The boat completes 5 downstream hours and 5 upstream hours:

5\times 16-5\times 12=80-60=20\text{km downstream}

Answer: Option 4 — 20 km downstream of A

Shortcut. Net drift per cycle \times number of cycles. A one-hour-each-way cycle displaces the boat by \left( \text{down}-\text{up}\right)=16-12=4 km downstream, and there are 5 cycles: 5\times 4=20 km.

The decisive step is arithmetic, not method: 96/6=16, not 18. Reading it as 18 gives 5\left( 18-12 \right)=30, which is not even an option — a useful signal that you have mis-divided. Options (a)–(c) are what you get from 4, 3 or 2.5 cycles.