# CBSE Class 10 Answered

**Quadratic Equations**

Given 2 8/11 = 30/11

Let q_{1}, q_{2} be the flow rates from two pipes, and cistern volume be V.

t_{1} = V/q_{1} and t_{2} = V/q_{2}

t_{1} + 1 = t_{2} ..... given than one pipe takes 1 min more to fill the cistern.

t = V/(q_{1} + q_{2}) ... time to fill the cistern together.

30/11 = V/(q_{1} + q_{2})

30/11 = 1/(q_{1}/V + q_{2}/V)

30/11 = 1/(1/t_{1} + 1/(t_{1} + 1))

30/11 = t_{1}(t_{1} + 1)/(2t_{1} + 1)

60t_{1}/11 + 30/11 = t_{1}(t_{1} + 1)

60t_{1}/11 + 30/11 = t_{1}^{2} + t_{1}

t_{1}^{2} - 49t_{1}/11 - 30/11 = 0

Solving this quadratic equation we find,

t_{1} = (49/11 ± 61/11)/2

t_{1} = 110/22 = 5 min and hence t_{2} = 6 min.

Hence the times in which each pipe will fill the cistern are 5 and 6 min respectively.

Regards,

Team,

TopperLearning.