Question

By walking at $\frac{3}{4}th$ of his usual speed, a man reaches office 20 minutes later than usual. What is his usual time?

• A. 30 minutes
• B. 60 minutes
• C. 70 minutes
• D. 50 minutes

Answer 1

The correct option is B 60 minutes

Let:
Distance covered be d
Usual speed be s
Usual time (in minutes) be t

Distance is the product of speed and time.
$d=st\left(i\right)$

When the person walks with $\frac{3}{4}th$ of his usual speed,
Speed is: $s_2=\frac{3}{4}s$
Time is: $t_2=t+20$
Again, applying distance formula:
$d=s_2{t}_2$
$d=\frac{3}{4}s(t+20)\left(ii\right)$

Equating equations (i) and (ii),
$\frac{3}{4}s(t+20))=st$
$\Rightarrow 3t+60=4t$
$\Rightarrow t=60\text{minutes}$