Question

Two taps, A and B, can fill a tank independently in 18 minutes and 21 minutes respectively, and tap C can empty the same tank in 42 minutes. If all three taps are turned on simultaneously, how long, in minutes, it will take for the tank to be filled?

Answer 1

• Tank fill with tap A and B in 18 minutes and 21 minutes Respectively
• tap C can empty the same tank in 42 minutes

$\\ {\pmb{\underline{\sf{Required \ Solution... }}}}$

If all the taps (A,B,C) will opens simultaneously then A and B will fill tank together but alongwith C will continuously decreasing the volume of water from the tank.

So, We've that:-

$\bullet \ {\pmb{\underline{\boxed{\sf{ Time_{(To \ fill \ Tank)} = \dfrac{abc}{ac+bc-ab} }}}}}$

$\\ \circ \ {\pmb{\underline{\sf{ According \ to \ Question: }}}} \\ \\ \\ \colon\implies{\sf{ \dfrac{18 \times 21 \times 42}{18 \times 42+21 \times 42 - 18 \times 21} }} \\ \\ \\ \colon\implies{\sf{ \dfrac{15876}{756+882-378} }} \\ \\ \\ \colon\implies{\sf{ \dfrac{15876}{1638-378} }} \\ \\ \\ \colon\implies{\sf{ \cancel{ \dfrac{15876}{1260} } }} \\ \\ \\ \colon\implies{\underline{\boxed{\sf{ 12.6 }}}}$

Hence,

Tank will take 12.6 minutes to fill completely.