CBSE Class 10 Answered
Given 2 8/11 = 30/11
Let q1, q2 be the flow rates from two pipes, and cistern volume be V.
t1 = V/q1 and t2 = V/q2
t1 + 1 = t2 ..... given than one pipe takes 1 min more to fill the cistern.
t = V/(q1 + q2) ... time to fill the cistern together.
30/11 = V/(q1 + q2)
30/11 = 1/(q1/V + q2/V)
30/11 = 1/(1/t1 + 1/(t1 + 1))
30/11 = t1(t1 + 1)/(2t1 + 1)
60t1/11 + 30/11 = t1(t1 + 1)
60t1/11 + 30/11 = t12 + t1
t12 - 49t1/11 - 30/11 = 0
Solving this quadratic equation we find,
t1 = (49/11 ± 61/11)/2
t1 = 110/22 = 5 min and hence t2 = 6 min.
Hence the times in which each pipe will fill the cistern are 5 and 6 min respectively.
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