Question

A man takes $6$ hours $30$ min in going by a cycle and coming back scooter. He would have lost $2$ hours $10$ min by going on cycle both ways. How long would it take him to go by scooter both ways?

• A. $2$ hrs
• B. $4\frac{1}{3}$ hrs
• C. $3\frac{1}{3}$ hrs
• D. $5\frac{1}{3}$ hrs

Answer 1

Answer: (B)

$4\frac{1}{3}$ hrs

Let time taken in going only by scooter be x hrs.Then, time taken for one way by cycle

$=[6\frac{1}{2}-x]hrs=[\frac{13}{2}-x]hrs$

Total time taken for going on cycle both ways$=6hrs30min+2hrs10min=8hrs40min=$$8\frac{40}{60}=8\frac{2}{3}hrs$

$\therefore 2\left[\frac{13}{2}-x\right]=8\frac{2}{3}\Rightarrow 13-2x=8\frac{2}{3}\Rightarrow 2x=13-8\frac{2}{3}=4\frac{1}{3}$ hrs

$\therefore$ It will take $4\frac{1}{3}$ hrs to go on scooter both ways.