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Question

# One tank can be filled up by two taps in 6 hours. The smaller tap alone takes 5 hours more than the bigger tap alone. Find the time required by each tap to fill the tank separately.

A
15 hrs and 10 hrs
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B
12 hrs and 13 hrs
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C
21 hrs and 4 hrs
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D
11 hrs and 14 hrs
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Solution

## The correct option is A 15 hrs and 10 hrsLet the tap to fill the tank be x.Smaller tap alone takes 5 hours more than the bigger tap alone = 1x+5Bigger tap can fill the tank = 1xOne tank can be filled up by two taps = 1x+1x+5=16⇒2x+5x2+5x=16⇒12x+30=x2+5xx2−7x−30=0Using −b±√b2−4ac2a to get the value for x⇒7±√(−7)2−4×1×(−30)2×1⇒7±√1692⇒7±132x=10, x=−3x cannot be negative.The time required by each tap to fill the tank separately = 15 hours and 10 hours.

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