# Discussion of Question with ID = 009 under Pipes-and-Cisterns

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### Question

A tank is filled in 6 minutes by three taps running together. Times taken by the three taps independently are in an AP[Arithmetic Progression], whose first term is a and common difference d. Then, a and d satisfy the relation?

A

a3 - 18a2 - ad2 + 6d2 = 0.

B

a3 - 12a2 + ad2 + 6d2 = 0.

C

a3 - 6a2 - ad2 + 6d2 = 0.

D

a3 - 30a2 + ad2 + 6d2 = 0.

Soln.
Ans: a

Let the times taken by the three taps be a - d, a and a + d. Then 6 minutes work of all the taps should add to 1. So we have, \$6 × 1/{a - d} + 6 × 1/a + 6 × 1/{a + d}\$ = 1, which is same as a3 - 18a2 - ad2 + 6d2 = 0.