. Three friends run around a circular track can complete a single loop in 24 minute, 32 minute &
56 minute respectively ,if they started running from the same initial points then after how
much time will meet together for first time
Answers
Answer:
lcm of 24 32 56 will be your answew
672 Mins will be taken to meet together for first time if Three friends run around a circular track can complete a single loop in 24 minute, 32 minute & 56 minute respectively and started running from the same initial points
Given:
Three friends run around a circular track
Time to complete a single loop in 24 minute, 32 minute & 56 minute respectively
Start from same initial point
To Find:
Time after which they will meet together for first time
Solution:
To Find time to meet at Start point for first time just find LCM (24 , 32 , 56)
24 = 2 * 2 * 2 * 3
32 = 2 * 2 * 2* 2 * 2
56 = 2 * 2 * 2 * 7
LCM = 2 * 2 * 2 * 2 * 2 * 3 * 7 = 672 Mins
After 672 Mins they will meet together for first time at start point
To Find meet together for first time anywhere on track
Assume loop is 672D m
Speed 1 = 672D/24 = 28D m/min
Speed 2 = 672D/22 = 21D m/min
Speed 3 = 672D/562 = 12D m/min
Relative speed of 1 and 2 = 28D - 21D = 7D m/min
Relative speed of 1 and 3 = 28D - 12D = 16D m/min
Time for 1 and 2 to meet = 672D/7D = 96 min
Time for 1 and 3 to meet = 672D/16D = 42 min
LCM (96 , 42) = Time to meet together for first time anywhere on track
LCM (96 , 42) = 672 Min
Time is same hence they will meet at starting point only for first time after 672 mins