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CAT 2018 Slot 2 — QA Question 1

Relative SpeedEasy

On a long stretch of east-west road, A and B are two points such that B is 350 km west of A. One car starts from A and another from B at the same time. If they move towards each other, then they meet after 1 hour. If they both move towards east, then they meet in 7 hrs. The difference between their speeds, in km per hour, is

Answer & solution

Correct answer: 50

Answer: 50

Solution

Easy

Let the two speeds be aa (from A) and bb (from B), with a>ba>b. Moving towards each other their speeds add; moving in the same direction (both east) the faster one closes the 350350 km gap. The "same direction" case gives the speed difference directly.

1

Both move east. Both cars travel east, so the car from A (the rear car, since B is west of A... A is east) — the gap of 350350 km is closed by the difference of speeds in 77 hours.

(a−b)×7=350(faster car closes the 350 km gap)⇒ a−b=3507⇒ a−b=50\begin{aligned} &(a-b)\times 7 = 350 \quad\text{(faster car closes the 350 km gap)}\\ &\Rightarrow\ a-b = \frac{350}{7}\\ &\Rightarrow\ a-b = 50 \end{aligned}
2

Cross-check (towards each other). When they approach, the combined speed covers 350350 km in 11 hour.

(a+b)×1=350⇒ a+b=350\begin{aligned} &(a+b)\times 1 = 350\\ &\Rightarrow\ a+b = 350 \end{aligned}

With a−b=50a-b=50 this gives a=200, b=150a=200,\ b=150 — consistent. The difference asked for is a−ba-b.

a−b=50 km/ha-b = 50\ \text{km/h}

Same direction ⇒\Rightarrow speeds subtract ⇒\Rightarrow difference =3507=50=\dfrac{350}{7}=50. You never even need the "towards each other" data.

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CAT 2018 Slot 2 QA Q1: On a long stretch of east-west road, A and B are two points such that B is 350 km west of A. One car starts fr — Solution | TheCATExam