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CAT 2020 Slot 2 — QA Question 21

Basics of TSD/ProportinalityEasy

The distance from B to C is thrice that from A to B. Two trains travel from A to C via B. The speed of train 2 is double that of train 1 while traveling from A to B and their speeds are interchanged while traveling from B to C. The ratio of the time taken by train 1 to that taken by train 2 in travelling from A to C is

Answer & solution

  • A

    4 : 1

  • B

    7 : 5

  • 5 : 7

  • D

    1 : 4

Solution

Easy

Assign convenient distances (AB=dAB=d, BC=3dBC=3d) and a base speed ss. Train 1 goes slow then fast; train 2 goes fast then slow (speeds swapped). Compute each total time as distance/speed and take the ratio.

1

Distances and speeds. BCBC is thrice ABAB, so AB=dAB=d, BC=3dBC=3d. On A→BA\to B let train 1's speed be ss and train 2's be 2s2s (double). Speeds swap on B→CB\to C: train 1 runs 2s2s, train 2 runs ss.

2

Time for train 1.

t1=ds+3d2s=2d+3d2s=5d2s\begin{aligned} &t_1 = \frac{d}{s} + \frac{3d}{2s} = \frac{2d+3d}{2s} = \frac{5d}{2s} \end{aligned}
3

Time for train 2.

t2=d2s+3ds=d+6d2s=7d2s\begin{aligned} &t_2 = \frac{d}{2s} + \frac{3d}{s} = \frac{d+6d}{2s} = \frac{7d}{2s} \end{aligned}
4

Ratio. The common d2s\tfrac{d}{2s} cancels.

t1:t2=5d2s:7d2s=5:7\begin{aligned} &t_1 : t_2 = \frac{5d}{2s} : \frac{7d}{2s} = 5 : 7 \end{aligned}
t1:t2=5:7t_1 : t_2 = 5 : 7
CAT 2020 Slot 2 QA Q21: The distance from B to C is thrice that from A to B. Two trains travel from A to C via B. The speed of train 2 — Solution | TheCATExam