1. P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can
work together for 4 days, what is the fraction of work left?
A. 8/15 B. 7/15 C. 11/15 D. 2/11
A. 8/15 B. 7/15 C. 11/15 D. 2/11
Answer : Option A
Explanation :
Total work =take L.C.M of15,20 = 60
Efficiency of work P can do in 1 day = 4
Efficiency of work Q can do in 1 day = 3
Amount of work P and Q can do in 1 day = 4+3=7
Amount of work P and Q can together do in 4 days = 4 ×7=28
Efficiency of work Q can do in 1 day = 3
Amount of work P and Q can do in 1 day = 4+3=7
Amount of work P and Q can together do in 4 days = 4 ×7=28
Fraction of work done = 28/60=8/15
Fraction of work left = 1 – 7/15= 8/15
Ie, the work will be done in 15 days
Answer : Option B
Amount of work A and B can together do in 1 day = 90/1+3=22 ½ days
Fraction of work left = 1 – 7/15= 8/15
2. P can lay railway track between two stations in 16 days. Q can do the same job
in 12 days. With the help of R, they completes the job in 4 days.
How much days does it take for R alone to complete the work?
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A. 9(3/5) days
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B. 9(1/5) days
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C. 9(2/5) days
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D. 10 days
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Answer : Option A
Explanation :
Total work =take L.C.M of16,12,4 =48
Efficiency of work P can do in 1 day = 3
Efficiency of work Q can do in 1 day = 4
Efficiency of work P, Q and R can together do in 1 day = 12
Efficiency of work R can do in 1 day = 12-(3+4) = 5
=> Hence R can do the job on 48/5 days = 9 (3/5) days
Efficiency of work Q can do in 1 day = 4
Efficiency of work P, Q and R can together do in 1 day = 12
Efficiency of work R can do in 1 day = 12-(3+4) = 5
=> Hence R can do the job on 48/5 days = 9 (3/5) days
3. P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need
to complete the work if P does the work and he is assisted by Q and R on every third day?
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A. 10 days
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B. 14 days
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C. 15 days
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D. 9 days
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Answer : Option C
Explanation :
Total work =take L.C.M of 20,30,60 = 60
Efficiency of work P can do in 1 day = 3
Efficiency of work Q can do in 1 day = 2
Efficiency of work R can do in 1 day = 1
P is working alone and every third day Q and R is helping him
Work completed in every 3 days = 2 × (3) + (3 + 2+ 1) = 12
So Total work completed =60/12=5*3=15
Efficiency of work R can do in 1 day = 1
P is working alone and every third day Q and R is helping him
Work completed in every 3 days = 2 × (3) + (3 + 2+ 1) = 12
So Total work completed =60/12=5*3=15
Ie, the work will be done in 15 days
4. A is thrice as good as B in work. A is able to finish a job in 60 days
less than B. They can finish the work in - days if they work together.
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A. 18 days
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B. 22 ½ days
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C. 24 days
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D. 26 days
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Answer : Option B
Explanation :
If A completes a work in 1 day, B completes the same work in 3 days
Hence, if the difference is 2 days, B can complete the work in 3 days
=> if the difference is 60 days, B can complete the work in 90 days
Hence, if the difference is 2 days, B can complete the work in 3 days
=> if the difference is 60 days, B can complete the work in 90 days
=> A can complete the work in 30 days
Total work =take L.C.M of 30,90 = 90
=> Efficiency of work B can do in 1 day=1
Efficiency of work A can do in 1 day = 3
Efficiency of work A can do in 1 day = 3
Amount of work A and B can together do in 1 day = 90/1+3=22 ½ days
5.If 10 men or 18 boys can do a work in 15 days, then the number of days required by 15 men and 33 boys to do twice the work is;
A. 9 B.36 C. 4 1/2 D.8
Answer : Option A
Explanation : 10 men = 18 boys
15 men =18*15 /10 =22
15 men + 33 boys = 27 +33 = 60 boys
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