Question

At the beginning of a journey, due to the breakdown of a car, its speed decreased by 20% and, thus, it took 30 minutes more to reach the destination. Find the actual time taken by the car for the entire journey.

• A. 2 hours
• B. 2.5 hours
• C. 3 hours
• D. 1.5 hours

Answer 1

The correct option is B 2.5 hours

Let the original time be T hours and the original speed be S km/hr.

So, distance = S × T km (1)

As there is a decrease in speed by 20%, so new speed = S × 80% $=\frac{4}{5}S$

Also, the increase in time is 30 minutes$=\frac{1}{2}hour$

$So,newtime=(T+\frac{1}{2})hours$

$Nowdistance,D=\frac{4}{5}S\times (T+\frac{1}{2})\left(2\right)$

On equating (1) and (2), we get

$S\times T=\frac{4}{5}S\times (T+\frac{1}{2})$

⇒ 5T = 4T + 2

⇒ T = 2 hours

Actual time taken = 2 hours + 30 minutes = 2.5 hours

Hence, option B is the correct answer.

Alternatively:
If the speed is decreased by 20%, then the time taken to cover a certain distance will increase by 25%.

So, if the original time taken is 4x, then the actual time taken will be 5x.

Now, 5x – 4x = 30 minutes

So, x = 30 minutes

Thus, actual time taken = 5x = 150 minutes = 2.5 hours.

Hence, option B is the correct answer.