SSC & BANK EXAMS: QUANTITATIVE APTITUDE · TIME, SPEED & DISTANCE

Relative speed, meeting point and average speed

Towards each other: time = distance ÷ (u + v). Chasing: gap ÷ (v − u). Round trip at u and v: average speed = 2uv/(u + v).

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Worked examples

Example 1 · level 1

Vihaan drives from Indore to Pune at 50 km/h and returns by the same road at 75 km/h. What is the average speed for the whole journey?

62.5 km/h
57 km/h
64 km/h
60 km/h

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Average speed = 2 × 50 × 75/(50 + 75)
= 7500/125 = 60 km/h.

Answer: 60 km/h

Example 2 · level 2

Bengaluru and Mysuru are 510 km apart. A bus leaves Bengaluru for Mysuru at 35 km/h and, at the same time, a car leaves Mysuru for Bengaluru at 50 km/h. How far from Bengaluru (in km) do they meet?

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Relative speed = 35 + 50 = 85 km/h.
Time = 510 ÷ 85 = 6 hours.
Bus covers 35 × 6 = 210 km from Bengaluru.

Answer: 210 km

Example 3 · level 3

A thief escapes from Chandni Chowk on a bike at 36 km/h. 2 hours later, a police jeep starts chasing him from the same place at 54 km/h. How many hours after the jeep starts will it catch the thief?

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Head start = 36 × 2 = 72 km.
Relative speed = 54 − 36 = 18 km/h.
Time = 72 ÷ 18 = 4 hours.

Answer: 4 hours