# A boy walked a certain distance. One third he walked at 10 km per hr. Another one fourth he waked at 20 km per hr. and the rest at 30 km per hr. Find

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A boy walked a certain distance. One third he walked at 10 km per hr. Another one fourth he waked at 20 km per hr. and the rest at 30 km per hr. Find the his average speed.

1. 730/43 km per hr
2. 720/42 km per hr
3. 73/3 km per hr
4. 720/43 km per hr

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Correct Answer - Option 4 : 720/43 km per hr

Given

Boy 1/3 distance walked at speed = 10 km per hr

Next 1/4 distance walked at speed = 20 km per hr

Rest distance walked at speed = 30 km per hr

Here, the man covers not equal distance at different speeds.

Let the distance be x km.

∴ Time is taken at 10 km per hr. distance one third (t1) = x/(3×10) hrs

Time is taken at 20 km per hr. distance one-fourth (t2) = x/(4×20)

Rest journey = x − (x/3 + x/4)

⇒ 5x/12

Rest journey time is taken at 30 km per hr. (t3) = 5x/(12×30) hrs

Total time is taken in the whole journey  = x/30 + x/80 + x/72

⇒ (24x + 9x + 10x)/720

⇒ 43x/720

Average speed is = (x)/43x/720

⇒ (720×x)/43x

⇒ 720/43 km per hr