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
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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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