IPMAT Indore 2022 · Quantitative Ability · Question 3

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

{t}_{12}=\frac{d}{12},{t}_{20}=\frac{d}{20}

Step 2 — use the one-hour saving.

\frac{d}{12}-\frac{d}{20}=1

Step 3 — combine the fractions. The lcm of 12 and 20 is 60:

\frac{5d-3d}{60}=1 \Rightarrow \frac{2d}{60}=1 \Rightarrow d=30

Check: \frac{30}{12}=2.5 hours and \frac{30}{20}=1.5 hours — a saving of exactly 1 hour ✔

Answer: 30 km

Shortcut. Use the product-over-difference shortcut. When the same distance is covered at speeds u and v with a time difference t,

d=\frac{uv}{v-u}\times t

Here \frac{12\times 20}{20-12}\times 1=\frac{240}{8}=30. One line, no fractions to clear.

This is worth drilling — it turns a two-step equation into a single mental calculation, and the same formula handles “arrives late/early by” questions.