how many hours will it take to fill the pool?

[yalanand]

Hose A can fill a 12x12x6 meter pool in 6 hours. Hose B can fill a 16x9x8 meter pool in 16 hours. If Jose uses both hoses to fill a 16x18x12 pool, how many hours will it take to fill the pool?

(A)8
(B)9
(C)12
(D)16
(E)18

[piyush_nitt]

Hose A can fill a 12x12x6 meter pool in 6 hours. Hose B can fill a 16x9x8 meter pool in 16 hours. If Jose uses both hoses to fill a 16x18x12 pool, how many hours will it take to fill the pool?

(A)8
(B)9
(C)12
(D)16
(E)18

Rate = Work done / time

here work done is filling of the pool

therefore rate at which hose A fills the pool = 12*12*6/6 = 144m^3/hr
similarly rate at which hose B fills the pool = 16*9*8/16 = 72m^3/hr

If both hoses to be used then total rate is = 144 + 72 = 216m^3 /hr

Time required to fill the pool using both hoses = 16x18x12/216 = 16 hrs

IMO D