Quantitative Aptitude Questions, Formulas & Shortcuts

Question 1

Medium

In a 1 km race, Usha beats Vani by 20 s and Wahida by 40 m. If Vani's speed is 4 m/s, by how many metres would Wahida beat Vani in a 1 km race?

A 41.67 m

B 40 m

C 43.48 m

D 38.4 m

Correct Answer: A

Explanation:

Vani's time = 1000/4 = 250 s, so Usha's time = 230 s; Wahida covers 960 m in 230 s. Wahida's time for 1000 m = 1000 × 230/960 = 239.58 s. In that time Vani covers 4 × 239.58 = 958.33 m, so Wahida beats her by 1000 − 958.33 = 41.67 m.

Question 2

Medium

Two runners start together from the same point on a 400 m track and run in the same direction at 6 m/s and 4 m/s. Which of the following statements is/are true? I. They first meet after 200 s. II. They meet only at the starting point. III. After 100 s they are diametrically opposite each other.

A Only I

B Only I and II

C Only I and III

D All of I, II and III

Correct Answer: D

Explanation:

Relative speed = 2 m/s, so the first meeting is at 400/2 = 200 s: I is true. Speed ratio 3 : 2 gives 3 − 2 = 1 meeting point, which must be the start (faster runner has done 3 laps at 200 s): II is true. At 100 s the gap is 2 × 100 = 200 m, half the track: III is true.

Question 3

Medium

In a 600 m backwater canoe race in Alappuzha, Thomas paddles at 3 m/s and Varghese at 2.5 m/s. Varghese is given a 20-second start. How far from the finish is the loser when the winner crosses the line?

A 100 m

B 25 m

C 60 m

D 50 m

Correct Answer: D

Explanation:

Thomas needs 600/3 = 200 s; Varghese needs 600/2.5 = 240 s, finishing 220 s after Thomas starts, so Thomas wins. At 200 s Varghese has paddled for 220 s and covered 2.5 × 220 = 550 m. He is 600 − 550 = 50 m from the finish.

Question 4

Medium

On a 500 m circular track, Neeraj starts 150 m ahead of Rohan, and both run in the same direction, Neeraj at 4 m/s and Rohan at 6.5 m/s. After how many seconds will Rohan catch Neeraj for the first time?

A 60 s

B 140 s

C 200 s

D 23.08 s

Correct Answer: A

Explanation:

Rohan must close the 150 m gap in front of him (not a full lap). Relative speed in the same direction = 6.5 − 4 = 2.5 m/s. Time = 150 ÷ 2.5 = 60 s.

Question 5

Easy

At a swimming gala, Lavanya swims 200 m in 2 min 40 s and Megha in 3 min 20 s. When Lavanya finishes, how many metres behind is Megha?

A 50 m

B 30 m

C 36 m

D 44 m

Correct Answer: E

Explanation:

Lavanya takes 160 s and Megha 200 s, so Megha swims at 200/200 = 1 m/s. In 160 s Megha covers 160 m. Megha is 200 − 160 = 40 m behind.

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