Question : In covering a distance of 50 km, Somya takes 1 hour more than Sunny. If Somya doubles his speed, then he would take 1 hour less than Sunny. Somya's speed is:
Option 1: 18.4 km/hr
Option 2: 12.5 km/hr
Option 3: 14.8 km/hr
Option 4: 15.6 km/hr
Correct Answer: 12.5 km/hr
Solution :
Let Somya's speed as $s$ km/hr and Sunny's time to cover the distance as $t$ hours.
We know that,
$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$
From the problem,
Somya takes 1 hour more than Sunny to cover the distance.
$⇒t = \frac{50}{s} - 1$
If Somya doubles his speed, he would take 1 hour less than Sunny.
$⇒t = \frac{50}{2s} + 1$
Setting these two equations equal to each other.
$⇒\frac{50}{s} - 1 = \frac{50}{2s} + 1$
$⇒\frac{50}{s} - \frac{25}{s} = 2$
$⇒\frac{25}{s} = 2$
$\therefore s= 12.5$ km/hr
Hence, the correct answer is 12.5 km/hr.
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