Question

The ratio of the speeds of Amar, Akabar and antony is $8:5:4$. If Akbar takes $15$min more than Amar to cover a certain distance, find the time taken by Antony to cover the same distance.

• A. $30$ minutes
• B. $60$ minutes
• C. $40$ minutes
• D. $50$ minutes

Answer 1

The correct option is D $50$ minutes

We know that $speed=\frac{distance}{time}time=\frac{distance}{speed}$

Let the speeds of Amar ,Akbar , Anthony be $8v,5v,4v$ respectively

and Let the Distance covered by all of them be $D$

Now, Akbar takes 15 minutes more than Amar

$\Rightarrow \frac{D}{5v}-\frac{D}{8v}=15\Rightarrow \frac{8D-5D}{40v}=15\Rightarrow \frac{3D}{40v}=15\Rightarrow D=200v.............\left(1\right)$

Now, Time taken by Antony to cover same distance

$T=\frac{D}{4v}=\frac{200v}{4v}=50minutes$