Question

The Strides of kapil and Rahul are in the ratio 3:4. In the same time as kapil takes 5 steps, Rahul takes only 4 steps.If they have to respective walk distances in the ratio 3:5, find the ratio of time taken by them?

Answer 1

Strides of both are in the ratio 3:4
If Kapil walks 3x cm in a step, then rahul can walk 4x steps in 1 step.
Kapil and rahul take 5 steps and 4 steps respectively in some time t.
Distance travelled by kapil in time t= 5 (3x)= 15x cm
Distance travelled by rahul in time t= 4 (4x)= 16x cm
Distance travelled by Kapil and Rahul in 1 unit of time will be $\left(\frac{15x}{t}\right)$ and $\left(\frac{16x}{t}\right)$ respectively.
Actual distance travelled by both of them is in the ratio 3:5.
Let the distance travelled by them be 3y and 5y.
Now the time taken by kapil to cover 3ycm=$\left[\frac{3y}{\left(\frac{15x}{t}\right)}\right]$
Time taken by rahul to cover 5y cm= $\left[\frac{5y}{\left(\frac{16x}{t}\right)}\right]$
Ratio of time taken by them=$\frac{\left[\frac{3y}{\left(\frac{15x}{t}\right)}\right]}{\left[\frac{5y}{\left(\frac{16x}{t}\right)}\right]}=\frac{16xyt}{25xyt}=\frac{16}{25}$