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Speed, Time, and Rest Ratio

XAT 2018 · Quantitative Ability & Data Interpretation · Medium · Quantitative Aptitude

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Every day a person walks at a constant speed, V1V_1 for 30 minutes. On a particular day, after walking for 10 minutes at V1V_1, he rested for 5 minutes. He finished the remaining distance of his regular walk at a constant speed, V2V_2, in another 30 minutes. On that day, find the ratio of V2V_2 and his average speed (i.e., total distance covered /total time taken including resting time).

  1. A.

    1:1

  2. B.

    1:2

  3. C.

    2:3

  4. D.

    2:1

  5. E.

    None of the above

Answer

A

Explanation

Regular distance = 30V130 V_1. On that day: Distance covered = 10V1+30V2=30V1  ⟹  30V2=20V1  ⟹  V1=1.5V210 V_1 + 30 V_2 = 30 V_1 \implies 30 V_2 = 20 V_1 \implies V_1 = 1.5 V_2. Total distance = 30V1=45V230 V_1 = 45 V_2. Total time = 10+5+30=4510 + 5 + 30 = 45 minutes. Average speed = 45V245=V2\frac{45 V_2}{45} = V_2. Ratio V2:Average Speed=V2:V2=1:1V_2 : \text{Average Speed} = V_2 : V_2 = 1:1.

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