Question

Saket runs twice on a circular track at a uniform speed. Bidhan starts at the same time as Saket and after Bidhan has completed one lap, he stops and Sunny starts and completes the second lap at a uniform speed. It is given that they start the race exactly at 2:30 pm and the track is 500 m in circumference. Sunny runs at a speed of 5 km/h greater than that of Bidhan and Saket's speed is 2 km/h greater than that of Bidhan. When does Saket finish the second lap if Sunny also finishes at the same time?

• A. 2 : 32 pm
• B. 2 : 35 pm
• C. 2 : 33 pm
• D. 2 : 36 pm

Answer 1

The correct option is B 2 : 35 pm

Let the speed of Bidhan be x km/h
Then, speed of Saket = (x + 2) km/h
And speed of Sunny = (x + 5) km/h
Time taken by Saket $=\frac{2\times 0.5}{x+2}hours$
Time taken by Bidhan $=\frac{0.5}{x}hours$
Time taken by Sunny $=\frac{0.5}{x+5}hours$
Now, $\frac{2\times 0.5}{x+2}=\frac{0.5}{x}+\frac{0.5}{x+5}\frac{1}{x+2}=\frac{1}{2x}+\frac{1}{2(x+5)}$
On solving, we get
x = 10 km/h
Hence, Saket's speed = 12 km/h
Therefore, Saket will finish the lap at 2:35 pm