Top 1,000+ UPSC Aptitude Questions and Answers - 1

Question: 1

A car covers a distance from Town I to Town II at the speed of 56 km/hr and from Town II to Town I at the speed of 53 km/hr. What is the average speed of the car?

(A) 53.5 km/hr

(B) 54.5 km/hr

(D) 55.5 km/hr

View Answer

Ans: B

Average speed = $$({2 × 56 × 53} / {56 + 53})$$ = $$({5936}/{109})$$ = 54.45 km/hr ≈ 54.5 km/hr.

Question: 2

A walks at a uniform rate of 4 km an hour and 4 hours after his start, B bicycles after him at the uniform rate of 10 km an hour. How far from the starting point will B catch A?

(A) 16.7 km

(B) 18.6 km

(D) 26.7 km

View Answer

Ans: D

Distance covered by A in 4 hrs = (4 × 4) km = 16 km.

Relative speed of B w.r.t. A = (10 - 4) km/hr = 6 km/hr.

Time taken to cover 16 km at relative speed = $$({16}/{6})$$hrs = $$({8}/{3})$$hrs.

Distance covered by B in $$({8}/{3})$$ hrs = $$(10 × {8}/{3})$$km = $$({80}/{3})$$km = 26.7 km.

Question: 3

Train A leaves Ludhiana for Delhi at 11 a.m, running at the speed of 60 km/hr. Train B leaves Ludhiana for Delhi by the same route at 2 p.m. on the same day, running at the speed of 72 km/hr. At what time will the two trains meet each other?

(A) 2 a.m. on the next day

(B) 5 a.m. on the next day

(D) none of these

View Answer

Ans: B

Distance covered by train A from 11 a.m. to 2 p.m.

i.e., in 3 hrs = (60 × 3) = 180 km.

Relative speed = (72 - 60) km/hr = 12 km/hr.

Time taken to cover 180 km at relative speed = $$({180}/{12})$$hrs = 15 hrs.

So, the two trains will meet 15 hrs after 2 p.m. i.e., at 5 a.m. on the next day.

Question: 4

Walking $${6}/{7}$$th of his usual speed, a man is 12 minutes too late. The usual time taken by him to cover that distance is

(A) 1 hour

(B) 1 hr 12 min

(D) 1 hr 20 min

View Answer

Ans: B

New speed = $${6}/{7}$$ of usual speed.

∴ New time = $${7}/{6}$$ of usual time.

∴ $$({7}/{6} of usual time)$$ – (usual time) = $${1}/{5}$$ hr.

⇔ $${1}/{6}$$ of usual time = $${1}/{5}$$ hr

⇔ usual time = $$({6}/{5})$$ = 1 hr 12 min.

Question: 5

A man in a train notices that he can count 21 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train travelling?

(A) 55 km/hr

(B) 58 km/hr

(D) 65 km/hr

View Answer

Ans: C

Number of gaps between 21 telephone posts = 20.

Distance travelled in 1 minute = (50 × 20)m = 1000 m = 1 km.

∴ Speed = 60 km/hr.

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Top 1,000+ UPSC Aptitude Questions and Answers - 1

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