Question

Rahul takes $6$ hours more than than Pathak to cover a distance of $540km$. If instead, Rahul doubles his speed, he would reach the destination one and a half hours before Pathak. Find Pathak's speed.

• A. $36$ kmph
• B. $60$ kmph
• C. $45$ kmph
• D. $40$ kmph

Answer 1

The correct option is A $36$ kmph

Given $S=540$

Time taken by Rahul $=6+x$

Time taken by Pathek $=x$

Rahul

$S=v\times t$

$540=v\times (6+x)$ …….$\left(1\right)$

If doubles his speed

$540=2v\times (x-\frac{3}{2})$ ………$\left(2\right)$

$\frac{\left(1\right)}{\left(2\right)}\Rightarrow \frac{\text{/}540}{\text{/}540}=\frac{\text{/}v(6+x)}{2\text{/}v(x-\frac{3}{2})}$

$2(x-\frac{3}{2})=6+x$

$2x-3=6+x$

$x=9$hrs.

Pathek's speed $\Rightarrow S=v_p\times x$

$\text{/}{540}_{60}=v_p\times \text{/}9$

$v_p=60$ kmph.