$A$ can complete a project in 20 days and $B$ can

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AAPL: Moderator; Posts: 2749; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Fri Jul 19, 2019 5:47 am

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GMAT Paper Tests

$A$ can complete a project in 20 days and $B$ can complete the same project in 30 days. If $A$ and $B$ start working on the project together and $A$ quits 10 days before the project is completed, in how many days will the project be completed?

A. 18 days
B. 27 days
C. 26.67 days
D. 16 days
E. 12 days

OA A

Source: Beat The GMAT — Problem Solving | Fri Jul 19, 2019 5:47 am

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by GMATGuruNY » Fri Jul 19, 2019 5:54 am

AAPL wrote:GMAT Paper Tests

$A$ can complete a project in 20 days and $B$ can complete the same project in 30 days. If $A$ and $B$ start working on the project together and $A$ quits 10 days before the project is completed, in how many days will the project be completed?

A. 18 days
B. 27 days
C. 26.67 days
D. 16 days
E. 12 days

Let the job = 60 units.
Rate for A alone = w/t = 60/20 = 3 units per day.
Rate for B alone = w/t = 60/30 = 2 units per day.
Since A quits 10 days before the project is completed, B works alone for 10 days.
Work completed by B alone in 10 days = r*t = 2*10 = 20 units.
Remaining work = 60-40 = 40 units.
These 40 units were completed by A+B working together (before A quit).
Combined rate for A+B working together = 3+2 = 5 units per day.
Time for A+B to complete 40 units = w/r = 40/5 = 8 days.

Total time = time for B alone + time for A+B together = 10+8 = 18 days.

The correct answer is A.

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by Scott@TargetTestPrep » Mon Jul 29, 2019 3:20 pm

AAPL wrote:GMAT Paper Tests

$A$ can complete a project in 20 days and $B$ can complete the same project in 30 days. If $A$ and $B$ start working on the project together and $A$ quits 10 days before the project is completed, in how many days will the project be completed?

A. 18 days
B. 27 days
C. 26.67 days
D. 16 days
E. 12 days

OA A

We are given that A can complete a project in 20 days and B can complete the same project in 30 days. Thus, the rate of A is 1/20 and the rate of B is 1/30. Since A quits 10 days before the project is completed, we can let t = the time in days worked by B, and thus, (t - 10) = the time in days worked by A. To determine t, we calculate the work done by A and the work done by B, using the work formula: work = rate x time.

work of A + work of B = 1

(1/20)(t - 10) + (1/30)(t) = 1

(t - 10)/20 + t/30 = 1

Multiplying the entire equation by 60, we have:

3t - 30 + 2t = 60

5t = 90

t = 18

Answer: A

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