Question : A man runs for 40 km. The time taken by him in the first 10 km is twice the time taken by him in the second 10 km. The time taken in the third 10 km is half of the time taken in the fourth 10 km, and the time taken in the fourth 10 km is equal to the time taken in the first 10 km. If his speed in the first 10 km is 40 km/hr, then what is the average speed for 40 km?
Option 1: 50 km/hr
Option 2: $\frac{70}{3}$ km/hr
Option 3: $\frac{160}{3}$ km/hr
Option 4: $40$ km/hr
Correct Answer: $\frac{160}{3}$ km/hr
Solution :
According to the question,
the speed in the first 10 km is 40 km/hr.
⇒ Time taken in first 10 km (T
1
) = $\frac{\text{Distance}}{\text{Speed}}$ = $\frac{10}{40}$ hours
The time taken in the first 10 km is twice the time taken in the second 10 km:
So, the time taken in the second 10 km (T
2
) = $\frac{T1}{2}$ = $\frac{10}{40 × 2}$ hours
and the time taken in the fourth 10 km (T
4
) = T
1
= $\frac{10}{40}$ hours
The time taken in the third 10 km (T
3
) is half of the time taken in the fourth 10 km:
⇒ T
3
= $\frac{T4}{2}$ = $\frac{10}{40×2}$
Total time = T1 + T2 + T3 + T4
= $\frac{10}{40}$ + $\frac{10}{40 × 2}$ × $\frac{10}{40 × 2}$ + $\frac{10}{40}$
= $\frac{2}{8}$ + $\frac{1}{8}$ × $\frac{1}{8}$ + $\frac{2}{8}$
= $\frac{6}{8}$
= $\frac{3}{4}$ hours
Now,
Average Speed = $\frac{\text{Total Distance}}{\text{Total Time}}$
= $\frac{40}{\frac{3}{4}}$
= $\frac{40 × 4}{3}$ = $\frac{160}{3}$ km/hr
Hence, the correct answer is $\frac{160}{3}$ km/hr.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
