Question

Anuj, Varun, Vansh can walk at the rates 3, 4, and 5 km an hour respectively. They start from a place at 1, 2, 3 hours respectively. When Varun catches Anuj, Varun sends him back with a message to Vansh. At what time does Vansh get the message ?

• A. 5 hrs 15 mins
• B. 3 hrs 30 mins
• C. 6 hrs 15 mins
• D. 5 hrs 45 mins

Answer 1

The correct option is A 5 hrs 15 mins

After 2 Hrs

For Anuj, distance travelled $=3\times 1=3Km$

For Varun, time $T$ when Varun catches Anuj $=4T-3T=3$ as Extra Distance to be Covered By Varun $=3km$

$\Rightarrow T=3hrs$

After Varun Catches Anuj ,$3hrs$ have passed and during this time Vansh Started walking and has been walked for $2Hrs$

Thus, Vansh Travelled $=5\times 2=10Km$

Now, Distance travelled by Anuj when he was caught by Varun $=12Km$

Now, distance between Vansh and Anuj $=12-10=2km$

Time $T_1$ taken by Anuj to meet Vansh

$=5T_1+3T_1=2Km\Rightarrow T_1=\frac{2}{8}=\frac{1}{4}=15min$

Total Time taken to Convey the message

$=2hrs$ (Varun Starts after this Time) $+3hrs$ (Varun Catches Anuj in this Time) $+15min$ (Anuj meet Vansh in this Time) $=5hrs$ $15min$

Therefore Answer is $\left(A\right)$