Clara can complete a job working alone in 48 days. Hugo can complete

Question

Clara can complete a job working alone in 48 days. Hugo can complete the same job working alone in 32 days. They begin working together, and after 8 days Hugo leaves. How many additional days will Clara, working alone, need to complete the remaining work?

A. 28
B. 32
C. 36
D. 40
E. 48

A. 28
B. 32
C. 36
D. 40
E. 48

M47-04

Bunuel · Accepted Answer

GMAT Club Official Solution:
  
Clara rate = 1/48
Hugo rate = 1/32

Together rate = 1/48 + 1/32 = 5/96

Work done in 8 days = 8* 5/96 = 5/12

Remaining work = 1 - 5/12 = 7/12

Time for Clara alone = (7/12)/(1/48) = 28

Answer: A.

Dereno · Answer

Clara can do the work in 48 hours

Hugo can do the work in 32 hours.

Let the total work be LCM (32,48) = 96 units.

The efficiency of Clara and Hugo are (96/48) = 2 units and (96/32) = 3 units respectively.

They both work together for 8 hours = 8*(3+2) = 40 units is completed.

Hugo leaves, so 96-40 = 56 units of work is to be completed by Clara working alone.

Time taken by Clara = 56/2 =  28 days.

Option A

Edskore · Answer

Great solutions above! Here's a slightly different way to think about this that some of you might find faster on test day.

Key Concept:  Combined Work Rates with a Worker Leaving Midway

1. Find individual rates as fractions of the job per day. 
Clara's rate = 1/48 per day
Hugo's rate = 1/32 per day

2. Find their combined rate. 
Together = 1/48 + 1/32
To add these, use LCD of 96:
= 2/96 + 3/96 = 5/96 per day

3. Calculate work done in the first 8 days (both working). 
Work completed = 8 × 5/96 = 40/96 = 5/12

4. Find remaining work. 
Remaining = 1 − 5/12 = 7/12

5. Calculate how long Clara takes to finish alone. 
Time = Remaining work ÷ Clara's rate = (7/12) ÷ (1/48) = (7/12) × 48 = 7 × 4 = 28 days

Answer: A (28)

The common trap here:  Many students calculate the total combined time (how long both would take to finish the entire job together) and then subtract 8, which gives a wrong answer. The question isn't asking how much faster they'd finish together — it's asking what happens when one person leaves partway through. You have to split the problem into two phases: the "together" phase and the "alone" phase.

Quick mental math shortcut:  Once you see that 5/12 of the work is done, the remaining 7/12 is just 7 × (48/12) = 7 × 4 = 28. Recognizing that 48 is divisible by 12 saves you from messy fraction division under time pressure.

Takeaway:  For any work-rate problem where workers join or leave partway through, always split the timeline into phases — calculate work done in each phase separately, then handle the leftover.

Clara can complete a job working alone in 48 days. Hugo can complete

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