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Question

A tank fills completely in 2 hours if both the taps are open. If only one of the taps is open at the given time, the smaller tap takes 3 hours more than the larger one to fill the tank. How much times does each tap take to fill the tank completely?

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Solution

Assume smaller tap take 'A' hours to fill larger tap " 'B' hours "
(1A+1B)×2=1

A=3+B

13+B+1B=12

B+3+B3B+B2=12

4B+6=3B+B2

B2B6=0

B23B+2B6=0

B(B3)2(B3)=0

(B3)(B+2)=0

B=32soB=3(+ve)

Smaller tap =6hrs.
larger tap =3hrs.

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