Question

Tom, Dick and Harry started out an a 100 km journey. Tom and Harry went by automobile at the rate of 25 km/hr, while Dick walked at the rate of 5 km/hr. After a certain distance, Harry got off and walked on at 5 km/hr, while tom went back for Dick and got him to the destination at the same time that Harry arrived. The number of hours required for the trip was:

• A. 5
• B. 6
• C. 7
• D. 8
• E. none of these

Answer 1

The correct option is D 8

Let Tom & Harry travels $x$ km, then Dick travels $\left(\frac{x}{5}\right)$ km

After Harry get off ride : Tom want back for Dick. They meet at same time

$\Rightarrow \frac{a}{5}=\frac{b}{25}$ & $a+b=\frac{4x}{5}$

$\Rightarrow a=\frac{2x}{15}$ , $b=\frac{10x}{15}$

So, Tom travels $\frac{10x}{15}$ km & Dick $\frac{2x}{15}$ km

Now, Time to reach destination for Harry done & (Tom + Dick) both is equal.

$\Rightarrow \frac{100-x}{5}=\frac{1}{25}(100-x+\frac{10x}{15})$

$\Rightarrow 500-5x=100-\frac{x}{3}\Rightarrow x=75$ km

Total time taken $=\frac{75}{25}+\frac{25}{5}=3+5=8$ hr.