In covering a distance of 192 km, Anmol takes 9 hours more than Nikhil. If Anmol doubles his speed, then he would take 7 hour less than Nikhil. Anmol's speed is:

Correct option is B

Given:

Distance = 192 km
Anmol takes 9 hours more than Nikhil:

If Anmol's speed doubles , he takes 7 hours less than Nikhil:

Formula Used:
Time =$$\frac{\text{ Distance }}{\text{ Speed}}$$​​

Solution:

Let Anmol's original speed be $$S_A$$​ and his time be $$T_A.$$​​
Let Nikhil's speed be $$S_N$$​ and his time be $$T_N.$$​​

​$$T_A = T_N + 9$$​

​$$\frac{1}{2} T_A = T_N - 7$$​

Using the given information, we can set up two equations based on Anmol's travel time:

Original time:

​$$\frac{192}{S_A} = T_N + 9$$​​

Doubled speed time:

​$$\frac{192}{2S_A} = T_N - 7$$​​

​$$\frac{96}{S_A} = T_N - 7$$​​

Now,

​$$\left(\frac{192}{S_A}\right) - \left(\frac{96}{S_A}\right) = (T_N + 9) - (T_N - 7)$$​​

​$$\frac{96}{S_A} = 9 - (-7)$$​​

​$$\frac{96}{S_A} = 16$$​

​$$S_A = \frac{96}{16} = 6 \text{ km/hr}$$​​

Anmol's speed is 6 km/hr.