Time and Work
- A and B can do a piece of work in 72 days. B and C can do it in 120 days and A and C can do it in 90 days. A alone can do it in :
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(A + B)’s 1 day’s work
= 1 ...........(i) 72
(B + C)’s 1 day’s work= 1 ...........(ii) 120
(C + A)’s 1 day’s work= 1 ...........(iii) 90
On adding all three,
2 (A + B + C)’s 1 day’s work= 1 + 1 + 1 72 120 90 = 5 + 3 + 4 = 12 = 1 360 360 30
∴ (A + B + C)’s 1 day’s work= 1 ...........(iv) 60
∴ A’s 1 day’s work
= Equation (iv) – (ii),= 1 - 1 = 2 - 1 = 1 60 120 120 120
∴ Required time = 120 daysCorrect Option: A
(A + B)’s 1 day’s work
= 1 ...........(i) 72
(B + C)’s 1 day’s work= 1 ...........(ii) 120
(C + A)’s 1 day’s work= 1 ...........(iii) 90
On adding all three,
2 (A + B + C)’s 1 day’s work= 1 + 1 + 1 72 120 90 = 5 + 3 + 4 = 12 = 1 360 360 30
∴ (A + B + C)’s 1 day’s work= 1 ...........(iv) 60
∴ A’s 1 day’s work
= Equation (iv) – (ii),= 1 - 1 = 2 - 1 = 1 60 120 120 120
∴ Required time = 120 days
- Ganesh, Ram and Sohan together can complete a work in 16 days. If Ganesh and Ram together can complete the same work in 24 days, the number of days Sohan alone takes, to finish the work is
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(Ganesh + Ram + Sohan)’s 1 day’s work
= 1 16
(Ganesh + Ram)’s 1 day’s work= 1 24
∴ Sohan’s 1 day’s work= 1 - 1 = 3 - 2 = 1 16 24 48 48
∴ Required time = 48 daysCorrect Option: B
(Ganesh + Ram + Sohan)’s 1 day’s work
= 1 16
(Ganesh + Ram)’s 1 day’s work= 1 24
∴ Sohan’s 1 day’s work= 1 - 1 = 3 - 2 = 1 16 24 48 48
∴ Required time = 48 days
- A and B together can do a piece of work in 12 days while A alone can do the same work in 30 days. B alone can do it in
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(A + B)’s 1 day’s work = 1 12 A’s 1 day’s work = 1 30 ∴ B’s 1 day’s work = 1 - 1 12 30 = 5 - 2 = 1 60 20
∴ Required time = 20 daysCorrect Option: B
(A + B)’s 1 day’s work = 1 12 A’s 1 day’s work = 1 30 ∴ B’s 1 day’s work = 1 - 1 12 30 = 5 - 2 = 1 60 20
∴ Required time = 20 days
- If 5 persons together can make 5 mats in 5 hours, then 10 persons in 10 hours will make
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∴ 5 : 10 
: : 5 : x 5 : 10
⇒ 5 × 5 × x = 10 × 10 × 5⇒ x = 10 × 10 × 5 = 20 mats 5 × 5 Correct Option: A
∴ 5 : 10 : : 5 : x 5 : 10
⇒ 5 × 5 × x = 10 × 10 × 5⇒ x = 10 × 10 × 5 = 20 mats 5 × 5
- A can do a piece of work in 10 days, B can do it in 12 days and C can do it in 15 days. In how many days will A, B and C finish it, working all together?
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A’s 1 day’s work = 1 10 B’s 1 day’s work = 1 12 C’s 1 day’s work = 1 15
∴ (A + B + C)’s 1 day’s work= 1 + 1 + 1 10 12 15 = 6 + 5 + 4 = 15 = 1 60 60 4
∴ Required time = 4 daysCorrect Option: D
A’s 1 day’s work = 1 10 B’s 1 day’s work = 1 12 C’s 1 day’s work = 1 15
∴ (A + B + C)’s 1 day’s work= 1 + 1 + 1 10 12 15 = 6 + 5 + 4 = 15 = 1 60 60 4
∴ Required time = 4 days
