Question

When a large pipe and a small pipe are opened for 4 hours and 9 hours respectively, a tank is half filled. but when both pipes are opened simultaneously the tank is filled in 12 hours. how many hours does the larger pipe take to fill the tank?

Answer 1

Part of the tank filled by the large pipe in 1 hr = x
Part of the tank filled by the small pipe in 1 hr = y


Part of the tank filled by the large pipe and small pipe in 1 hr = 1/12
=> x + y = 1/12 ------(1)

Part of the tank filled by the large pipe in 4 hr + Part of the tank filled by the small pipe in 9 hr = 1/2
=> 4x + 9y = 1/2 ----(2)

Solve (1) and (2) for x
(1)×9 - (2) => 5x = 9/12 - 1/2
5x = 1/4
x = 1/20

i.e., part of the tank filled by the large pipe in 1 hr = 1/20
=> large pipe alone needs 20 hours to fill the tank

Answer 2

A lens with one convex and one concave side is convex-concave or meniscus. It is this type of lens that is most commonly used in corrective lenses. If the lens is biconvex or plano-convex, a collimated beam of light passing through the lens converges to a spot (a focus) behind the lens.