IPMAT Indore 2026 · Quantitative Ability · Question 13

Step 1 — express both times. Let the distance be d km.

\text{Man’s time}=\frac{d}{4}\text{hours}, \text{Woman’s time}=\frac{d}{6}\text{hours}

Step 2 — work out the total time gap. The woman starts 30 minutes later and finishes 20 minutes earlier, so her journey is shorter by

30+20=50\text{minutes}=\frac{5}{6}\text{hours}

Step 3 — form the equation.

\frac{d}{4}-\frac{d}{6}=\frac{5}{6}

Step 4 — solve. The left side is d\left( \frac{3-2}{12}\right)=\frac{d}{12}:

\frac{d}{12}=\frac{5}{6}\Rightarrow d=10

Check: man takes 10/4=2.5 h =150 min; woman takes 10/6\approx 100 min but starts 30 min later, finishing at 130 min — exactly 20 min before him. ✓

Answer: 10

Shortcut. The only real trap is the time gap: it is 30+20=50 minutes, not 20 and not 10. Once you see that, \frac{d}{4}-\frac{d}{6}=\frac{d}{12} makes the arithmetic a single step.