Question

There are two tanks A and B. of the same capacity. One pipe which can fill at the
rate of 2 litres per minute takes 165 minutes to fill tank A. Tank B has N pipes,
numbered from 1 to N. fitted to it. The i pipe. where 1<=i<=N, can fill he tank in
(24+ i) litres per hour. All the pipes are opened simultaneously and B is filled after
one hour. Find N.
​

Answer 1

Given : There are two tanks A and B. of the same capacity. One pipe which can fill at the rate of 2 litres per minute takes 165 minutes to fill tank A. Tank B has N pipes, numbered from 1 to N. fitted to it. The i pipe. where 1<=i<=N, can fill he tank in (24+ i) litres per hour. All the pipes are opened simultaneously and B is filled after one hour.

To Find :  N.

Solution:

One pipe which can fill at the rate of 2 litres per minute takes 165 minutes to fill tank A.

=> tank capacity  = 165 * 2 = 330  litre

1<=i<=N, can fill he tank in (24+ i) litres per hour.

(24 + 1)  + (24 + 2) + (24  + 3)  + ..   + (24 + b)  litres in 1 hrs

= 24N  + N(N + 1)/2  = 330

=> 48N + N²  + N = 660

=> N² + 49N - 660  = 0

=>  N² + 60N - 11N - 660  = 0

=> (N + 60)(N - 11) = 0

=> N = 11

11 pipes

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