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CBSE Class 10 Answered

A,B AND C START CYCLING AROUND A CIRCULAR PATH IN THE SAME DIRECTION AT SAME TIME. CIRCUMFERENCE OF THE PATH IS 1980M. IF THE SPEED OF A IS 330M/MIN , SPEED OF B IS 198M/MIN AND C IS 220M/MIN AND THEY START FROM THE SAME POINT THEN AFTER WHAT TIME INTERVAL THEY WILL BE TOGETHER AT THE STARTING POINT.
Asked by rushi chincholkar | 01 Jun, 2013, 07:56: PM
answered-by-expert Expert Answer
A will complete one round in 1980/330 = 6 min 
B will complete one round in 1980/198 = 10 min 
C will complete one round in 1980/220 = 9 min 
 
Now, let A, B and C meet after time t and they would have respectively completed, n1, n2 and n3 rounds and they would be be x distance away from the start point
 
Hence, 330t = x + 1980n1
198t = x + 1980n2
220t = x + 1980n3
 
Substituting x from equation 1 into 2 and 3
198t = 330t - 1980n1 + 1980n2
1980(n1-n2) = 132t
t = 15(n1-n2)
 
Also,  220t = 330t - 1980n1 + 1980n3
1980(n1-n3) = 110t
Since t is same, and n1-n3 and n1-n2 can be any whole number, so we need to compute LCM of 15 and 18 which is 90

Hence, A,B and C will meet after 90 min. 
Answered by | 02 Jun, 2013, 05:41: AM

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