(Q)A, B, and C can do a work separately in 16, 32, and 48 days respectively. They started the work together but B left off 8 days and C 6 days before the completion of the work. In what time is the work finished?
Solution:
[Concept– B work complete होने के 8 days before चला जाता है तो work करने के लिए अब सिर्फ A and C बचा| so work done by (A+C) in 1 day=6+2=8 unit ∴ work done by (A+C) in 2 day=8×2=16 unit. remaining work=96-16=80 unit. यहाँ पर A and C का 2 days का ही work निकाला गया है क्योंकि question में कह रहा है कि work complete होने से 6 days before फिर C चला जाता है that means B के जाने के 2 days बाद ही C चला जाता है| अब last का 6 days work करने के लिए सिर्फ A ही बच जाता है| so work done by A in 6 day=6×6=36 unit. remaining work=80-36=44 unit.ये 44 unit work A, B and C ने मिलकर किया है |]
Work done by (A+C) in 1 day=6+2=8 unit
∴ Work done by (A+C) in 2 day=8×2=16 unit.
Remaining work=96-16=80 unit.
Work done by A in 6 day=6×6=36 unit
Remaining work=80-36=44 unit.
Time taken by (A+B+C)=44/11
=4 days
Total days=2+6+4=12 days Ans.
Method-2
Let the whole work be completed in x days
According to the question,
(Q)A, B and C can complete a work in 10, 12 and 15 days respectively. A left the work 5 days before the work was completed and B left 2 days after A had left. Number of days required to complete the whole work is:
Solution:
[Concept- A work complete होने के 5 days before चला जाता है तो work करने के लिए अब सिर्फ B and C बचा| so work done by (B+C) in 1 day=5+4=9 unit ∴ work done by (B+C) in 2 day=9×2=18 unit. remaining work=60-18=42 unit. यहाँ पर B and C का 2 days का ही work निकाला गया है क्योंकि question में कह रहा है कि B left 2 days after A had left means A के जाने के 2 days बाद ही B चला जाता है that means work complete होने में 3 days बचा ही था कि B work छोड़ चला जाता है | अब last का 3 days work करने के लिए सिर्फ C ही बच जाता है| so work done by C in 3 day=4×3=12 unit. remaining work=42-12=30 unit.ये 30 unit work A, B and C ने मिलकर किया है |]
Work done by (B+C) in 1 day=5+4=9 unit
∴ Work done by (B+C) in 2 day=9×2=18 unit.
Remaining work=60-18=42 unit
now,
Work done by C in 3 day=4×3=12 unit
Remaining work=42-12=30 unit
Time taken by (A+B+C)=30/15
=2 days
Total days=2+3+2=7 days Ans.
Method-2
Let the whole work be completed in x days
According to the question,
(Q)A, B, and C can do a piece of work in 10, 12, and 15 days respectively.They began the work together but B leaves after two days, how long would it take A and C to finish the Remaining work?
Solution:
Note: [L.C.M of 10,12,15=60 and 60/10=6, 60/12=5, 60/15=4]
Total work done by A, B, and C in 1 day=(6+5+4)unit=15 unit
[Concept: B 2 days बाद work छोड़ देता है, it means B के work छोडने से पहले A, B, and C तीनों 2 days तक एक साथ work किया होगा| so total work done by A, B, and C in 2 days=15×2=30 unit. Remaining work=60-30=30 unit. जब B work छोड़ दिया तो सिर्फ अब A and C बचा है तो total work done by A and C in 1 day=6+4=10 unit ]
Total work done by A, B, and C in 2 day=15×2=30 unit
Remaining work=60-30=30 unit
When B left the job then
Total work done by A and C in 1 day=6+4=10 unit
Time taken by A and C=30/10
=3 days Ans.
(Q)A, B, and C can do a piece of work in 20, 25, and 30 days respectively.They began the work together but C leaves after 3 days. In how many days the whole work was completed?
Solution:
Note: [L.C.M of 20,25,30=300 and 300/20=15, 300/25=12, 300/30=10]
Work done by A, B, and C in 1 day=(15+12+10)unit=37 unit
[Concept: C 3 days बाद work छोड़ देता है, it means C के work छोडने से पहले A, B, and C तीनों 3 days तक एक साथ work किया होगा| so total work done by A, B, and C in 3 days=37×3=111 unit. Remaining work=300-111=189 unit. जब C work छोड़ दिया तो सिर्फ अब A and B बचा है तो total work done by A and B in 1 day=15+12=27 unit.]
Total work done by A, B, and C in 3 day=37×3=111 unit
Remaining work=300-111=189 unit
When C left the work then
Work done by A+B in 1 day=15+12=27 unit
Time taken by (A+B)=189/27
=7 days
The whole work was completed in=3+7
=10 days Ans.
(Q)A, B, and C together can do a piece of work in 40 days. After working with A, B and C for 16 days, A leaves and then B and C complete the remaining work in 40 days more. A alone could do the work in.
Solution:
Let work done by (A+B+C) in per day=1 unit
Total work done by (A+B+C) in 40 day=40 unit
Total work done by (A+B+C) in 16 day=16 unit
Now,
Remaining work=40-16=24 unit
[Concept: 24 unit work अब सिर्फ B and C करेगा जिसे करने में B and C को 40 days लग रहा है क्योंकि A ने work छोड़ दिया है |]
work done by B and C in 40 days =24 unit
work done by B and C in 1 day =24/40
=0.6 unit
Efficiency(eff.) of A=Eff. of(A+B+C)-Eff. of (B+C)
= 1-0.6=0.4 unit per day
Time taken by A=40/0.4=100 days Ans.
(Q)A, B, and C can do a job in 6 days, 12 days and 15 days respectively. After 1/8 of the work is completed, C leaves the job. Rest of the work is done by A and B together. Time taken to finish the work is.
Solution:
[Concept: 60×(1/8)=7.5 unit. जब 7.50 unit work complete हो गया तब C ने job छोड़ दिया now remaining work=60-7.50=52.50 unit. 52.50 unit work सिर्फ A and B मिलकर कर रहा है|]
Now,
60×(1/8)=7.5 unit
Remaining work=60-7.50=52.50 unit
Work done by A +B in 1 days=10+5=15 unit
Time taken by (A+B)=52.50/15
=7/2=3 ½ days Ans.
The common and frequently asked a question of Time And Work Problem with solution and Shortcut Tricks for Bank PO, SSC CGL, SSC CHSL, Railway Exam Type-3.1.
(Q)A, B, and C can do a piece of work in 15, 20, and 12 days respectively. They began the work together but A left 5 days before completion of the work. In how many days was the work done?
Solution:
Note: [L.C.M of 15,20,12=60 and 60/15=4, 60/20=3, 60/12=5]
[Concept: A work complete होने के 5 days पहले चला जाता है तो work complete होने में जो 5 days बचा था तो उसमे सिर्फ B and C ने ही work किया so, work done by B and C in 1 days=3+5=8 unit ∴work done by B and C in 5 days=8×5=40 unit. remaining work 60-40=20 unit. 20 unit work A, B, and C ने मिलकर किया होगा ]
Work done by B and C in 1 day=(3+5)unit=8 unit
Total work done by B and C in 5 day=8×5=40 unit
Remaining Work=60-40=20 unit
Work done by A, B, and C in 1 day=(4+3+5)unit=12 unit
Now,
20 unit work is done by A, B and C so,
Time taken by (A+B+C)=20/12
=5/3 days
Total time=5+(5/3)
=20/3 days Ans.
(Q)A, B, and C can do a piece of work in 24, 30, and 40 days respectively. They began the work together but C left 4 days before completion of the work. In how many days was the work done?
Solution:
[Concept: C work complete होने के 4 days पहले चला जाता है तो work complete होने में जो 4 days बचा था तो उसमे सिर्फ A and B ने ही work किया so, work done by A and B in 1 days=5+4=9 unit ∴work done by A and B in 4 days=9×4=36 unit. remaining work 120-36=84 unit. 84 unit work A, B, and C ने मिलकर किया होगा ]
Work done by A and B in 1 day=(5+4)unit=9 unit
Total work done by A and B in 4 day=9×4=36 unit
Remaining Work=120-36=84 unit
Work done by A, B, and C in 1 day=(5+4+3)unit=12 unit
Now,
84 unit work is done by A, B and C so,
Time taken by (A+B+C)=84/12
=7 days
Total time=4+7=11 days Ans.
The common and frequently asked a question of Time And Work Problem with solution and Shortcut Tricks for Bank PO, SSC CGL, SSC CHSL, Railway Exam Type-3.2.
(Q)A, B, and C can complete a work separately in 24, 36, and 48 days respectively. They started work together but C left after 4 days of start and A left 3 days before the completion of the work. In how many days will the work be completed.
Solution:
[Concept: C work start होने के 4 days बाद work छोड़ कर चला जाता है| it means C के जाने से पहले A, B, and C ने 4 days तक एकसाथ work किया है so, work done (A+B+C) in 1 day=(6+4+3)=13 unit ∴work done (A+B+C) in 4 day=13×4=52 unit Remaining work=144-52=92 unit.]
Work done (A+B+C) in 1 day=(6+4+3)=13 unit
Work done (A+B+C) in 4 day=13×4=52 unit
Remaining work=144-52=92 unit.
[concept: C तो पहले ही जा चुका है अब सिर्फ A and B बचा है. now question में कह रहा है A work complete होने से 3 days पहले चला जाता है तो last 3 days सिर्फ B ने ही work किया होगा so work done by B in 3 days=3×4=12 unit. remaining work=92-12=80 unit. 80 unit work A and B ने मिलकर किया है |]
Now,
Work done by B in 3 days=3×4=12 unit
Remaining work=92-12=80 unit
Work done by (A+B) in 1 day=(6+4)=10 unit
Time taken by (A+B)=80/10
=8 days
Total time=(4+3+8)=15 days Ans.
Users Today : 154
Total views : 468554