Two workers, A and B, completed a job in 10 days, but A did not work

Question

Two workers, A and B, completed a job in 10 days, but A did not work during the last 2 days. In the first 7 days they together completed 4/5 of the job. How long would A take to do the job alone?

A. 16 days
B. 15 days
C. 14 days
D. 13 days
D. 12 days

stne · Answer

Total  10   days - in which  8  days were together and  2  days B worked alone

Given  7  days working together -  \frac{4}{5}   work done

1   day working together  = \frac{4}{35}  work done

in  8  days working together  = \frac{4 *8 }{35}= \frac{32}{35}

Hence in Last two days ONLY B worked and completed remaining  \frac{3}{35}

B will do whole work alone in  = \frac{35 *2 }{3} = \frac{70}{3}  days.

Hence B's rate  = \frac{3}{70}

We know in  7  days  \frac{4}{5}   work was done :

This can be represented by:

Hence  \frac{1}{A}+\frac{1}{B} = \frac{4}{35}

\frac{1}{A}+ \frac{3}{70}= \frac{4}{35}

\frac{1}{A} = \frac{4}{35} - \frac{3}{70}

\frac{1}{A}=\frac{1}{14}

A=14

Ans C

luisdicampo · Answer

Deconstructing the Question

Let the whole job be  1 .
A and B finish in 10 days, but A does not work during the last 2 days (days 9 and 10).

In the first 7 days, working together, they complete  \frac{4}{5}  of the job, so we can find the combined rate  A+B .
Then use the remaining work to find  B  from the last 2 days, and finally get  A .

Step-by-step

From the first 7 days:

7(A+B) = \frac{4}{5}

A+B = \frac{\frac{4}{5}}{7} = \frac{4}{35}

Remaining work after 7 days:

1 - \frac{4}{5} = \frac{1}{5}

From day 8 to day 10, they complete this remaining  \frac{1}{5} .
Day 8: both work, so they do  \frac{4}{35} .
Days 9 and 10: only B works, so they do  2B .

\frac{4}{35} + 2B = \frac{1}{5}

2B = \frac{1}{5} - \frac{4}{35} = \frac{7}{35} - \frac{4}{35} = \frac{3}{35}

B = \frac{\frac{3}{35}}{2} = \frac{3}{70}

Now:

A = (A+B) - B = \frac{4}{35} - \frac{3}{70} = \frac{8}{70} - \frac{3}{70} = \frac{5}{70} = \frac{1}{14}

So A alone needs:

\frac{1}{\frac{1}{14}} = 14  days.

Answer: C

Edskore · Answer

The concept being tested here is Work and Rate Problems with a split-timeline setup — a classic GMAT Focus twist where two workers don't work together the entire time.

The key is to break the job into two phases and let total work = 1.

Step 1 — Extract the combined rate from the first 7 days.

In the first 7 days, A and B work together and complete 4/5 of the job.

Combined rate (A + B) per day = (4/5) ÷ 7 = 4/35 of the job per day.

Step 2 — Map out the full 10-day timeline.

"A did not work during the last 2 days" means A is absent on days 9 and 10.

- Days 1–8: both A and B work → 8 × (4/35) = 32/35 of the job done
- Days 9–10: only B works → remaining work = 1 − 32/35 = 3/35

B alone completes 3/35 of the job in 2 days → B's rate = 3/70 per day.

Step 3 — Isolate A's rate.

A + B = 4/35, and B = 3/70.

A = 4/35 − 3/70 = 8/70 − 3/70 = 5/70 = 1/14 per day.

A alone takes 14 days → Answer: C.

Common trap: The most frequent mistake is misreading "last 2 days" as days 8 and 9 instead of days 9 and 10, which throws off how much B works alone. Always anchor your timeline to the full job length first — the last 2 days of a 10-day job are days 9 and 10, full stop.

Takeaway: In split-timeline Work and Rate problems, set total work = 1, extract the combined rate from the phase where both workers are present, then use remaining work to isolate each individual rate.

Edskore · Answer

This is a classic Work and Rate problem with a split timeline — the kind where GMAT Focus loves to hide the trick in the middle of the setup. Let me share a framing that makes it almost mechanical.

Step 1 — Assign total work = 1, and name the rates.
Let A's rate = a (work/day), B's rate = b (work/day).

Step 2 — Read the timeline carefully.
"A did not work during the last 2 days" means days 9 and 10.
So: Days 1–8: both A and B work. Days 9–10: only B works.

Step 3 — Use the given: in the first 7 days they completed 4/5 of the job.
7(a + b) = 4/5
→ a + b = 4/35

Step 4 — Account for the remaining work.
Remaining after day 7 = 1 − 4/5 = 1/5.
This 1/5 is done over days 8, 9, and 10:
- Day 8: both work → 4/35 of the job
- Days 9–10: only B works → 2b of the job

So: 4/35 + 2b = 1/5
→ 2b = 1/5 − 4/35 = 7/35 − 4/35 = 3/35
→ b = 3/70

Step 5 — Solve for A.
a = 4/35 − 3/70 = 8/70 − 3/70 = 5/70 = 1/14

A alone would take 14 days. Answer: C.

The common trap: Most people read "last 2 days" and assume A stopped working on day 8 as well, treating days 8–10 as all-B. Re-read carefully — "last 2 days" of a 10-day job means days 9 and 10 only. Always map the timeline explicitly before writing equations.

Takeaway: In split-timeline work problems, draw out which workers are active on which days first — one misread of the timeline sends your whole solution off track.

— Kavya | 725 (Q90, V85, DI79) | GMAT Focus Edition

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