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A plumber is twice efficient than his apprentice. After the plumber

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KarunMendiratta
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A plumber is twice efficient than his apprentice. After the plumber [#permalink] New post   28 Mar 2021, 22:42
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A plumber is twice efficient than his apprentice. After the plumber has worked alone for \(2\) hours, his apprentice joins him and working together they complete the job \(3\) hours later.

Quantity A
Quantity B
Number of hours required for apprentice alone to finish the job
10


A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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Re: A plumber is twice efficient than his apprentice. After the plumber [#permalink] New post   30 Mar 2021, 01:08
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If rate at which plumber works is 2x, rate at which apprentice works is x.

Working together at x+2x = 3x rate for 3 hours, they finished 3*3x = 9x work together. Working alone, apprentice will finish 9x work in 9x÷x = 9 hours.

Also, if plumber does a job in 2 hours, the apprentice is definitely going to take 4 hours, given the plumber is twice as efficient.

Therefore, the apprentice alone will take 9+4 = 13 hours. Hence, A is the correct answer.

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Re: A plumber is twice efficient than his apprentice. After the plumber [#permalink] New post   30 Mar 2021, 02:40
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Explanation:

More efficient means less time or more work!

Let us assume it takes the plumber alone \(x\) hours to finish the job
So his apprentice would require \(2x\) hours to finish the same job

Work done by Plumber + Work done by the apprentice = 1
\(W_p + W_a = 1\)

The plumber has worked for a total of \(5\) hours whereas, his apprentice worked for \(3\) hours only
i.e. \(\frac{5}{x} + \frac{3}{2x} = 1\)
\(13 = 2x\)
\(x = 6.5\)

Col. A: \(2(6.5) = 13\)
Col. B: \(10\)

Hence, option A
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Re: A plumber is twice efficient than his apprentice. After the plumber [#permalink] New post   30 Mar 2021, 07:56
KarunMendiratta wrote:
Explanation:

More efficient means less time or more work!

Let us assume it takes the plumber alone \(x\) hours to finish the job
So his apprentice would require \(2x\) hours to finish the same job

Work done by Plumber + Work done by the apprentice = 1
\(W_p + W_a = 1\)

The plumber has worked for a total of \(5\) hours whereas, his apprentice worked for \(3\) hours only
i.e. \(\frac{5}{x} + \frac{3}{2x} = 1\)
\(13 = 2x\)
\(x = 6.5\)

Col. A: \(2(6.5) = 13\)
Col. B: \(10\)

Hence, option A


Excellent solution!
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Re: A plumber is twice efficient than his apprentice. After the plumber [#permalink] New post   28 Aug 2022, 12:47
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In total, the plumber worked 5 hours, and the apprentice worked 3 hours.
If the apprentice did it alone, he would put in twice the time the plumber put in, plus the time the apprentice already put in, which is 2*5 +3 = 13 hours.

So A is bigger.
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Re: A plumber is twice efficient than his apprentice. After the plumber [#permalink] New post   16 Nov 2022, 09:06
I don't like the wording, honestly! Because "finish the job" could mean how long would it take for the apprentice to finish (working alone) if the plumber left after two hours. In that case, the answer is 9. Which is annoying. So, hopefully on the test it is a bit clearer.
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Re: A plumber is twice efficient than his apprentice. After the plumber [#permalink] New post   11 Feb 2024, 00:47
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Re: A plumber is twice efficient than his apprentice. After the plumber [#permalink]
11 Feb 2024, 00:47
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