In covering a distance of 162 km, Abhay takes 6 hours more than Sameer. If Abhay doubles his speed, then he would take 3 hours less than Sameer. Abhay's initial speed is:​

Correct option is D

Given:

Distance = 162 km

Abhay takes 6 hours more than Sameer.

If Abhay doubles his speed, he takes 3 hours less than Sameer.

Formula Used:

Time = Distance ÷ Speed

Solution: 

​Let Sameer's speed be x km/h

Let Abhay's speed be y km/h 

From first condition: 

​$$\frac{162}{y} - \frac{162}{x} = 6 \quad \text{(i)}$$​​

From second condition:

​$$\frac{162}{x} - \frac{81}{y} = 3 \quad \text{(ii)}$$​​

Add equations (i) and (ii):

​$$\left(\frac{162}{y} - \frac{162}{x}\right) + \left(\frac{162}{x} - \frac{81}{y}\right) = 6 + 3 \\ \ \\ \frac{162 - 81}{y} = 9 \\ \ \\ \frac{81}{y} = 9 \\ \ \\ y = \frac{81}{9} = 9$$​​

Abhay's initial speed is 9 km/h