The speeds of A and B are in the ratio 3 : 4 (A is slower). A takes 20 minutes more than B to reach the same place. Find the actual times taken by A and by B, respectively, to reach that place (give answers in minutes).

Introduction / Context:
This is a classic time–speed–distance ratio problem. If two people cover the same distance with speeds in a fixed ratio, then their times are in the inverse ratio. The given 20-minute gap anchors the absolute values.

Given Data / Assumptions:

• Speed(A) : Speed(B) = 3 : 4.
• A is slower; A takes 20 minutes more than B.
• Both cover the same distance D.

Concept / Approach:
Times are inversely proportional to speeds: Time(A) : Time(B) = 1/3 : 1/4 = 4 : 3. Let times be 4x and 3x. Their difference equals 20 minutes, which gives x and hence the actual times.

Step-by-Step Solution:

Verification / Alternative check:
Let speeds be 3k and 4k; times are D/(3k) and D/(4k). Difference D(1/3k − 1/4k) = D/(12k) must equal 20 min; choosing D/k = 240 gives times 80 and 60 min, consistent with the ratio 4:3.

Why Other Options Are Wrong:

• 40 & 30, 90 & 45, 90 & 50, 72 & 54 do not keep a 4:3 time ratio while also differing by exactly 20 minutes.

Common Pitfalls:
Inverting the ratio incorrectly; applying the 20-minute difference to speeds instead of times.

Final Answer:
80 min and 60 min