question_answer

A, B and C go walking round a circle 1 km in circumference at the rates of 10 m/min, 20 m/min and 40 m/min, respectively. If they all start together and walk in the same direction, when will they be together at the same place?

A) After 50 min

B) After 100 min

C) After 240 min

D) After 800 min

Correct Answer: B

Solution :

[b] Time taken by A, B, C to make a round \[=\frac{1000}{10}\min ,\] \[=\frac{1000}{20}\min ,\] \[=\frac{1000}{40}\min ,\] = 100 min, 50 min, 25 min Required time = LCM of 100 min, 50 min, 25 min \[=(5\times 5\times 2\times 2)=100\,\,\text{min}\] Hence, they will be together at the starting point after 100 min.