Question

The distance covered for a race is $1$ km. When $A$ and $B$ run the race, $A$ wins by $40$ metres. When $A$ and $C$ run, then $A$ wins by $70$ metres. When $B$ and $C$ run

• A. $B$ wins by $110$ m
• B. $C$ wins by $100$ m
• C. $B$ wins by $31\frac{1}{4}$ m
• D. $C$ wins by $50$ m

Answer 1

Answer: (C)

$B$ wins by $31\frac{1}{4}$ m

When $A$ and $B$ run
$A:B=1000:960$
When $A$ and $C$ run
$A:C=1000:930$
When $B$ and $C$ run
$B$ win by $\frac{960-930}{960}\times 1000$
$B$ win by $C$ $=\frac{30}{960}\times 1000$
$B$ win by $C$ $=31\frac{1}{4}$