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A can complete a certain job in 12 days

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by BTGmoderatorDC » Sat Mar 03, 2018 3:44 am
A can complete a certain job in 12 days. B is 60% more efficient than A. In how many days can B complete the same job?

(A) 6
(B) 6.25
(C) 7
(D) 7.5
(E) 4.8

Can some experts show me how to solve it?

OA D
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by GMATGuruNY » Sat Mar 03, 2018 4:16 am
lheiannie07 wrote:A can complete a certain job in 12 days. B is 60% more efficient than A. In how many days can B complete the same job?

(A) 6
(B) 6.25
(C) 7
(D) 7.5
(E) 4.8
Since B is 60% more efficient that A, we get:
B's rate = (160/100)(A's rate) = (8/5)(A's rate).
Rate and time have a RECIPROCAL RELATIONSHIP.
Since B's rate is 8/5 of A's rate, B's time is 5/8 of A's time:
(5/8)(12) = 15/2 = 7.5 days.

The correct answer is D.
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by swerve » Sat Mar 03, 2018 4:35 am
We know that A complete the job in 12 days, that's mean that the A's rate = 1/12 work/days.

If B is 60% more efficient than A, then the B's rate will be
$$\frac{1}{12}\cdot(60\%)+\frac{1}{12}=\frac{2}{15}\ \frac{work}{days}.$$
Finally, B can complete the same job in, Time = work / Rate = 15/2 = 7.5 days.
$$Rate_B\ =\ \frac{work}{time}\ \Rightarrow \frac{2}{15}=\frac{work}{time}\ \Rightarrow time_B=\frac{15}{2}days=7.5days$$
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by Jeff@TargetTestPrep » Thu Mar 08, 2018 4:39 pm
lheiannie07 wrote:A can complete a certain job in 12 days. B is 60% more efficient than A. In how many days can B complete the same job?

(A) 6
(B) 6.25
(C) 7
(D) 7.5
(E) 4.8
The rate of A is 1/12.

Since B is 60% more efficient the rate of B is 1.6 x 1/12 = 1.6/12 = 16/120 = 2/15.

Since time is inverse of rate, B can complete the job in 15/2 = 7.5 days.

Answer: D

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