Question : In a race of 1200 m, Ram can beat Shyam by 200 m or by 20 sec. What must be the speed of Ram?
Option 1: 14 m/sec
Option 2: 12 m/sec
Option 3: 10 m/sec
Option 4: 16 m/sec
Correct Answer: 12 m/sec
Solution :
Ram beats Shyam by 200 m or 20 sec. This means Shyam covers a 200 m distance in 20 sec. $\therefore$ Speed of Shyam = $\frac{200}{20}$ = 10 m/sec Also, in the 1200 m race, Ram beats Shyam by 200 m. Distance covered by Ram = 1200 m Distance covered by Shyam in same time = 1000 m Now, the 1000 m distance is covered by Shyam with a speed of 10 m/sec in $\frac{1000}{10}$ = 100 seconds So, 1200 m distance is covered by Ram in 100 seconds. $\therefore$ Speed of Ram = $\frac{1200}{100}$ = 12 m/sec Hence, the correct answer is 12 m/sec.
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