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Question:

Once upon a time, in a jungle, a rabbit and a tortoise planned a 5-kilometre. The rabbit dashed off and soon took a huge lead. He realized that even after taking a rest for ‘x’ mins, he would still beat the tortoise by 10 mins, he sat under a tree and went to sleep. Meanwhile the tortoise kept walking slowly and went past the sleeping rabbit. When the rabbit woke up, he realized that he had slept for (20 + x) mins, and immediately started running towards the target at a speed 5/3 times his original speed. The race eventually ended in a dead heat. If the ratio of the original speed of the rabbit to that of the tortoise was 5 : 1 and the rabbit overstretched his nap by 1 2/3 x mins, then how long did the rabbit take to complete the race?

Explanation:

The rabbit overstretched his sleeping time by 1 $\frac{2}{3}$ x mins.
∴ x + 1 $\frac{2}{3}$ x = 20 + x
⇒ x = 12 mins

Let the speed (in km/min) of the rabbit and tortoise be ‘5s’ and ‘s’ respectively.

Had the rabbit not overstretched his nap, he would have beaten the tortoise by 13 min.
∴ $\frac{5}{5 s}$ + 10 + 12 = $\frac{5}{s}$
⇒ s = $\frac{2}{11}$

Hence, the time taken by the tortoise to complete the race = $\frac{5}{s}$ = $\frac{5}{2 / 11}$ = 28 mins 30 seconds.
This is also the time taken by Rabbit to complete the race since the race ended in a dead heat.

Hence, option (b).

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