Question

The speeds of $A$ and $B$ are in the ratio $3:4.$ $A$ takes $20$ minutes more than $B$ to reach a destination. In what time does $A$ reach the destination?

• A. $1\frac{1}{3}$ hours
• B. $2$ hours
• C. $1\frac{2}{3}$ hours
• D. $2\frac{2}{3}$ hours

Answer 1

The correct option is A $1\frac{1}{3}$ hours

Let the time taken by A be $x$ hrs.

Then,

$\text{Time taken by B}=(x-\frac{20}{60})hrs=(x-\frac{1}{3})hrs$

Ration of speeds = Inverse ratio of times

$\Rightarrow (x-\frac{1}{3}):x\Rightarrow \frac{x-\frac{1}{3}}{x}=\frac{3}{4}$

$\Rightarrow \frac{3x-1}{3x}=\frac{3}{4}\Rightarrow 12x-4=9x$

$\Rightarrow 3x=4\Rightarrow x=\frac{4}{3}=1\frac{1}{3}hrs$