Pipes A and B together can fill an empty tank in 
minutes. If A take 3 minutes more than B to fill the tank, then the time (as minutes) in which A alone would fill one-third part of the tank is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 5
| Understanding | Application | |||||||||||
| Tricks |
Let B can fill the tank in x min Then A can fill in x + 3 min
In one min A + B can work x + (x + 3) = 2x + 3 unit So In 20/3 min 20/3(2x + 3) = total work ⇒ 20/3(2x + 3) = x(x + 3) ⇒ 40x/3 + 20 = x2 + 3x ⇒ 40x + 60 = 3x2 + 9x ⇒ 3x2 + 9x - 40x - 60 = 0 ⇒ 3x2 - 31x - 60 = 0 |
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| Now |
After solving equation x = 12 So efficiency of A = 12 unit in one min & the efficiency of B (12 + 3) unit in one min 15 unit |
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| Hence |
total work = x(x + 3) = 12 × 15 So 1/3 of total work = 12 × 15 × 1/3 = 12 × 5 unit Here 12 × 5 unit work by A So time = 12 × 5/12 = 5 min |