A person travelling by car covers a distance of 125 km in time t1. When he…

2020

A person travelling by car covers a distance of 125 km in time t1. When he decreases his speed by 20%, the time taken to cover the same distance is t2. The ratio t2 : t1 is:

  1. A.

    5 : 2

  2. B.

    4 : 5

  3. C.

    5 : 4

  4. D.

    2 : 5

Attempted by 4 students.

Show answer & explanation

Correct answer: C

CONCEPT: For a fixed distance, distance = speed × time. Therefore, when the distance is unchanged, speed × time remains constant and time changes inversely with speed.

APPLICATION:

  1. Let the original speed be v. The original time is t1 = 125/v.

  2. After a 20% decrease, the new speed is 80% of v, which is 4v/5.

  3. The new time is t2 = 125/(4v/5) = 125 × 5/(4v) = (5/4)t1.

  4. So t2 : t1 = (5/4)t1 : t1 = 5 : 4.

CROSS-CHECK: If v = 100 km/h, then t1 = 1.25 h. At 80 km/h, t2 = 1.5625 h, and 1.5625 : 1.25 simplifies to 5 : 4.

Result: 5 : 4.

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