Question : Aman and Kapil start from Delhi and Gwalior, respectively, towards each other at the same time. They meet at Mathura and then take 196 minutes and 225 minutes, respectively, to reach Gwalior and Delhi. If the speed of Aman is 30 km/h, what is the speed (in km/h) of Kapil?
Option 1: $28$
Option 2: $30$
Option 3: $\frac{225}{7}$
Option 4: $\frac{392}{15}$
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Correct Answer: $28$
Solution :
Given:
Aman and Kapil start from Delhi and Gwalior, respectively, towards each other at the same time.
Time taken by Aman to reach Gwalior after reaching Mathura = 196 mins
Time taken by Kapil to reach Delhi after reaching Mathura = 225 mins
Formula Used:
Let the speed of Kapil be $v$ km/hr
When two person after meeting take $t_{1}$ and $t_{2}$ hours to reach the destination, then $\frac{v_{1}}{v_{2}}=\frac{\sqrt{t_{2}}}{\sqrt{t_{1}}}$
Calculation:
Speed of Aman = 30 km/h
$\frac{v_{1}}{v_{2}}=\frac{\sqrt{t_{2}}}{\sqrt{t_{1}}}$
$⇒\frac{30}{v}=\frac{\sqrt{225}}{\sqrt{196}}$
$⇒\frac{30}{v}=\frac{15}{14}$
$⇒v=\frac{30 \times14}{15}$
$⇒v=28$ km/h
Hence, the correct answer is 28 km/h.
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