Question

$A$ and $B$ run a kilometer and $A$ wins by $25$ seconds. $A$ and $C$ run a kilometer and $A$ wins by $275$ m.

$B$ and $C$ run the same distance and $B$ wins by $30$ sec. What is the time taken by $A$ to run a kilometer ?

• A. $2$ min $25$ sec
• B. $2$ min $50$ sec
• C. $3$ min $20$ sec
• D. $3$ min $30$ sec

Answer 1

The correct option is A $2$ min $25$ sec

If $A$ covers a distance of $1$ km in $x$ seconds, then $B$ covers the distance of $1$ km in $(x+25)$ seconds.
If $A$ covers a distance of $1$ km then in the same time $C$ covers only $725$ metres
If $B$ covers the distance of $1$ km in $(x+25)$ seconds, then $C$ covers the distance of $1$ km in $(x+55)$ seconds.

Also $C$ covers a distance of $725$ metres in $x$ seconds.

Then $\frac{x}{725\times 1000}=x+55$

$\Rightarrow x=145$
$\Rightarrow$ $A$ covers a distance of $1$ km in $145$ seconds, i.e., $2$ min $25$ sec.