Question

in covering a distance of 30 km ajay takes 2 hours more than sameer if ajay doubles his speed,then he would take 1hr less than sameer.ajay's speed is

this is direct and inverse properties

Answer 1

Given :

Total distance = d = 30 km

Ajay takes 2 hours more than sameer

Ajay doubles his speed,then he would take 1hr less than sameer

To Find :

The speed of Ajay

Solution :

Let The speed of Sameer = s km/h

The speed of Ajay = a km/h

Let the time taken by Sameer = x hours

Let The time taken by Ajay = y hours

Statement I

∵  Time taken by Ajay = 2 + time taken by Samer

i.e      y = 2 + x

∵  speed = $\dfrac{distance}{time}$

For Ajay

    a = $\dfrac{30}{y}$

Or,   a = $\dfrac{30}{2+x}$              .........1

For Sameer

     s = $\dfrac{30}{x}$

Statement II

Ajay doubles his speed,then he would take 1hr less than sameer

For Ajay

     a = $\dfrac{30}{y}$

Or,  2 a = $\dfrac{30}{x-1}$              .........2

For Sameer

     s = $\dfrac{30}{x}$

Solving eq 1 and eq 2

i.e   2 × $\dfrac{30}{2+x}$  = $\dfrac{30}{x-1}$  

or,   $\dfrac{60}{2+x}$  = $\dfrac{30}{x-1}$  

Or,  2 ( x - 1 ) = 2 + x

Or,  2 x - 2 = 2 + x

Or,  2 x - x = 2 + 2

Or,          x = 4 hours

i,e Time taken by Sameer = x = 4 hours

Now, Put the value of x into eq 2

So, 2 a = $\dfrac{30}{x-1}$  

Or,  2 a = $\dfrac{30}{4-1}$

Or,  2 a = $\dfrac{30}{3}$

∴     2 a = 10

Or,     a = $\dfrac{10}{2}$ = 5 km/h

i.e   Speed of Ajay = a = 5 km/h

Hence, The Speed of Ajay in covering 30 km distance is 5 km/h   Answer