Aman takes 36 minutes more than Sudhanshu to cover a distance of 130 km. if Aman doubles his speed, he takes 42 minutes less than Sudhanshu to cover the same distance. To cover the distance of 195 km, how much time (in hours) will Sudhanshu take with his same speed?

Correct option is D

Given:

Distance D = 130 km.

Aman’s time is 36 min more than Sudhanshu’s.

If Aman doubles speed, his time is 42 min less than Sudhanshu’s.

Find Sudhanshu’s time for 195 km at the same speed.

Formula Used:

Time t =$$\dfrac{D}{\text{speed}}$$​​

Solution:

Let Sudhanshu’s speed = v  km/h and Aman’s speed = u km/h.

Convert minutes to hours: 36 min=0.6 h, 42 min=0.7  h

​Set up equations using $$t_A=130/u; t_S=130/v$$​​

​$$\frac{130}{u}=\frac{130}{v}+0.6 \quad (1)$$​​

​$$\frac{130}{2u}=\frac{130}{v}-0.7 \quad (2)$$​​
From (2): $$\frac{130}{u}-\frac{260}{v}=-1.4$$​​
Subtract (1): $$\left(\frac{130}{u}-\frac{260}{v}\right)-\left(\frac{130}{u}-\frac{130}{v}\right)=-1.4-0.6$$​​
​$$-\frac{130}{v}=-2 \implies \frac{130}{v}=2 \implies v=65$$​​

Sudhanshu’s time for 195 km:
t$$=\frac{195}{65}=3\text{ hours}.$$​​