A is 3 times as efficient as B. Together they finish a work in 9 days. How long would A alone take?
Solution
If B takes x days, A takes x/3. Together: 4/x per day = 1/9, so x = 36.
A takes 12 days and B 36 days.
Answer: (C) 12 days
Quantitative Aptitude · Work and motion
Time and Work: MAH CET, NMAT and SNAP practice questions
20 questions in the pattern of MAH MBA CET, NMAT and SNAP. Each question is marked with the exams it suits. Answer it, then open the step-by-step solution.
Exam:
24 men can finish a job in 20 days. How many days will 10 men take?
Solution
Work = 24 × 20 = 480 man-days.
Days = 480/10 = 48.
Answer: (C) 48 days
A and B together can complete a task in 20 days, and A alone can complete it in 24 days. How long will B alone take?
Solution
B per day = 1/20 − 1/24 = 1/120.
B takes 120 days.
Answer: (C) 120 days
A and B can do a work in 10 and 30 days. They start together, but A leaves 2 days before the work is finished. In how many days is the work completed?
Solution
Let T be the total. A works T − 2 days, B works T days: (T − 2)/10 + T/30 = 1.
Solving gives T = 9 days.
Answer: (B) 9 days
A and B can do a work in 24 and 12 days. They start together, but A leaves 5 days before the work is finished. In how many days is the work completed?
Solution
Let T be the total. A works T − 5 days, B works T days: (T − 5)/24 + T/12 = 1.
Solving gives T = 9 2/3 days.
Answer: (C) 9 2/3 days
10 men working 9 hours a day can complete a piece of work in 12 days. In how many days can 24 men working 5 hours a day complete twice that work?
Solution
M₁D₁H₁/W₁ = M₂D₂H₂/W₂.
D₂ = 10 × 12 × 9 × 2/(24 × 5) = 18.
Answer: (C) 18 days
A and B together can complete a task in 12 days, and A alone can complete it in 15 days. How long will B alone take?
Solution
B per day = 1/12 − 1/15 = 1/60.
B takes 60 days.
Answer: (D) 60 days
A can finish a work in 30 days and B in 6 days. In how many days can they finish it together?
Solution
Together per day: 1/30 + 1/6 = 1/5.
Time = 5 days.
Answer: (A) 5 days
A and B can finish a work in 18 and 12 days. They work together for 3 days, then A leaves. In how many days in all is the work finished?
Solution
In 3 days they finish 5/12.
B finishes the remaining 7/12 in 7 days. Total = 10 days.
Answer: (A) 10 days
A can do a work in 6 days and B in 8 days. They work on alternate days, with A starting. In how many days will the work be finished?
Solution
Every 2 days they do 1/6 + 1/8 = 7/24. After 6 days, 7/8 is done.
The remaining 1/8 takes 3/4 more day(s). Total = 6.75 days.
Answer: (B) 6.75 days
A can do a work in 4 days and B in 8 days. They work on alternate days, with A starting. In how many days will the work be finished?
Solution
Every 2 days they do 1/4 + 1/8 = 3/8. After 4 days, 3/4 is done.
The remaining 1/4 takes 1 more day(s). Total = 5 days.
Answer: (B) 5 days
30 men begin a work that they can finish in 30 days. After 15 days, 15 more men join them. In how many days in all is the work finished?
Solution
Total work = 30 × 30 = 900 man-days; 450 done in 15 days.
The rest, 450, is done by 45 men in 10 days. Total = 25 days.
Answer: (D) 25 days
A is 2 times as efficient as B. Together they finish a work in 12 days. How long would A alone take?
Solution
If B takes x days, A takes x/2. Together: 3/x per day = 1/12, so x = 36.
A takes 18 days and B 36 days.
Answer: (B) 18 days
12 men can finish a job in 20 days. How many days will 6 men take?
Solution
Work = 12 × 20 = 240 man-days.
Days = 240/6 = 40.
Answer: (B) 40 days
A and B can do a job in 12 and 8 days. With C's help, they finish it in 3 days and are paid Rs. 4800. What is C's share?
Solution
In 3 days A does 1/4 and B does 3/8 of the work.
C does the rest, 3/8, so C gets 3/8 × 4800 = 1800.
Answer: (D) Rs. 1800
A can do a work in 20 days and B in 12 days. Together they earn Rs. 3600 for it. What is A's share?
Solution
Shares ∝ work per day: 1/20 : 1/12 = 12 : 20.
A's share = 12/32 × 3600 = 1350.
Answer: (B) Rs. 1350
12 men working 9 hours a day can complete a piece of work in 20 days. In how many days can 24 men working 6 hours a day complete the same work?
Solution
M₁D₁H₁/W₁ = M₂D₂H₂/W₂.
D₂ = 12 × 20 × 9 × 1/(24 × 6) = 15.
Answer: (A) 15 days
A and B can do a job in 12 and 10 days. With C's help, they finish it in 3 days and are paid Rs. 9600. What is C's share?
Solution
In 3 days A does 1/4 and B does 3/10 of the work.
C does the rest, 9/20, so C gets 9/20 × 9600 = 4320.
Answer: (D) Rs. 4320
A and B can finish a work in 20 and 30 days. They work together for 3 days, then A leaves. In how many days in all is the work finished?
Solution
In 3 days they finish 1/4.
B finishes the remaining 3/4 in 22.5 days. Total = 25.5 days.
Answer: (D) 25.5 days
A can do a work in 15 days and B in 10 days. Together they earn Rs. 2400 for it. What is A's share?
Solution
Shares ∝ work per day: 1/15 : 1/10 = 10 : 15.
A's share = 10/25 × 2400 = 960.
Answer: (C) Rs. 960
These are original practice questions written by Target Campus in the pattern and difficulty of MAH MBA CET, NMAT, SNAP and other MBA entrance tests. They are not previous-year papers.
Preparing for MAH CET, NMAT, SNAP or CAT? Courses, live classes and mocks by Dr. Kiran Derle at Target Campus.
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