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Oppenheimer1945
Joined: 16 Jul 2019
Last visit: 16 Apr 2026
Posts: 786
Given Kudos: 236
Location: India
Schools: INSEAD '26 (D) ISB '27 (D) IIMB '26 (A) IIMA '26 (A) HEC '26 (D) LBS '26 IESE '27 (D) Fuqua '27 (WL) Tepper '27 (WL)
GMAT Focus 1: 645 Q90 V76 DI80 
GPA: 7.81
Schools: INSEAD '26 (D) ISB '27 (D) IIMB '26 (A) IIMA '26 (A) HEC '26 (D) LBS '26 IESE '27 (D) Fuqua '27 (WL) Tepper '27 (WL)
GMAT Focus 1: 645 Q90 V76 DI80
Posts: 786
26 Dec 2024, 10:24
Kudos
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Let total work be 300
A rate=6/hr
B rate=5/hr
C rate=4/hr
A+B+C= 15/hr
for 10 hr, 150 work done
remaining work=150
B stopped 15hr before completion
Let total time be T,
B+C worked for T-15 hrs : work done =9(T-15)=9T-225
C worked for 15 hrs: work done=60
90 units completed by B+C: 9(T-15)=90 => T=25hrs
Total time=10+25=35hrs
C)
A rate=6/hr
B rate=5/hr
C rate=4/hr
A+B+C= 15/hr
for 10 hr, 150 work done
remaining work=150
B stopped 15hr before completion
Let total time be T,
B+C worked for T-15 hrs : work done =9(T-15)=9T-225
C worked for 15 hrs: work done=60
90 units completed by B+C: 9(T-15)=90 => T=25hrs
Total time=10+25=35hrs
C)
26 Dec 2024, 10:24
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Bookmarks
Let's define 1 the total amount of work and x the total hours required to finish the task.
Then, productivity of machine A is 1/50 and so on.
\(\frac{1}{50} * 10 + \frac{1}{60} * (x - 15) + \frac{1}{75} * x = 1\),
\(3x = 105\)
\(x = 35\)
Answer: C
Then, productivity of machine A is 1/50 and so on.
\(\frac{1}{50} * 10 + \frac{1}{60} * (x - 15) + \frac{1}{75} * x = 1\),
\(3x = 105\)
\(x = 35\)
Answer: C
26 Dec 2024, 10:31
Kudos
Bookmarks
The stem tells us that;
And we have to select;
Work=Rate*Time
W=A*50 or B*60 Or C*75
Let the total time be T.
Also,W=(A+B+C)*10 + (B+C)(T-15-10) + C*15
Solving above equation;
W = 10A - 15B + T(B+C)
W = 10(W/50) - 15(W/60) + T { (W/60) +(W/75)}
1 = 10(1/50) - 15(1/60) + T { (1/60) +(1/75)}
Solving this;
T=35
- Machine A, working alone, can complete a task in 50 hours
- Machine B, working alone, can complete the same task in 60 hours
- Machine C, working alone, can complete it in 75 hours
- All three machines started working together on the task
- Machine A stopped working after 10 hours
- Machine B stopped 15 hours before the task was completed
And we have to select;
- How many total hours were required to finish the task
Work=Rate*Time
W=A*50 or B*60 Or C*75
Let the total time be T.
Also,W=(A+B+C)*10 + (B+C)(T-15-10) + C*15
Solving above equation;
W = 10A - 15B + T(B+C)
W = 10(W/50) - 15(W/60) + T { (W/60) +(W/75)}
1 = 10(1/50) - 15(1/60) + T { (1/60) +(1/75)}
Solving this;
T=35
