Time and Work
- A and B together can do a work in 8 days, B and C together in 6 days while C and A together in 10 days, if they all work together, the work will be completed in :
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(A + B)'s 1 day's work = 1 .....(i) 8 (B + C)'s 1 day's work = 1 .....(ii) 6 (C + A)'s 1 day's work = 1 .....(iii) 10
On adding all three equations ,2(A + B + C)'s 1 day's work = 1 + 1 + 1 8 6 10 2(A + B + C)'s 1 day's work = 15 + 20 + 12 = 47 120 120 ⇒ (A + B + C)'s 1 day’s work = 47 240
Correct Option: C
(A + B)'s 1 day's work = 1 .....(i) 8 (B + C)'s 1 day's work = 1 .....(ii) 6 (C + A)'s 1 day's work = 1 .....(iii) 10
On adding all three equations ,2(A + B + C)'s 1 day's work = 1 + 1 + 1 8 6 10 2(A + B + C)'s 1 day's work = 15 + 20 + 12 = 47 120 120 ⇒ (A + B + C)'s 1 day’s work = 47 240 ∴ (A + B + C) together will complete the work in 240 = 5 5 days. 47 47
Second method to solve this question ,
Here , x = 8 , y = 6 , z = 10Time taken = 2xyz xy + yz + zx Time taken = 2 × 8 × 6 × 10 8 × 6 + 6 × 10 + 10 × 8
Time taken = 960 48 + 60 + 80 Time taken = 960 188 Time taken = 240 = 5 5 days. 47 47
- A and B can do a piece of work in 12 days, B and C in 8 days and C and A in 6 days. How long would B take to do the same work alone ?
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(A + B)'s 1 day's work = 1 .....(i) 12 (B + C)'s 1 day's work = 1 .....(ii) 8 (C + A)'s 1 day's work = 1 .....(iii) 6
On adding,2(A + B + C)'s 1 day's work = 1 + 1 + 1 12 8 6 2(A + B + C)'s 1 day's work = 2 + 3 + 4 = 9 24 24 ∴ (A+ B + C)'s 1 day’s work = 9 = 9 .....(iv) 24 × 2 48
On, subtracting (iii) from (iv),B’s 1 day’s work = 9 - 1 48 6 B’s 1 day’s work = 9 - 8 = 1 48 48
∴ B can complete the work in 48 days.
Second method to solve this question ,
Here , x = 12 , y = 8 , z = 6Time taken = 2xyz - xy + yz + zx
Correct Option: D
(A + B)'s 1 day's work = 1 .....(i) 12 (B + C)'s 1 day's work = 1 .....(ii) 8 (C + A)'s 1 day's work = 1 .....(iii) 6
On adding,2(A + B + C)'s 1 day's work = 1 + 1 + 1 12 8 6 2(A + B + C)'s 1 day's work = 2 + 3 + 4 = 9 24 24 ∴ (A+ B + C)'s 1 day’s work = 9 = 9 .....(iv) 24 × 2 48
On, subtracting (iii) from (iv),B’s 1 day’s work = 9 - 1 48 6 B’s 1 day’s work = 9 - 8 = 1 48 48
∴ B can complete the work in 48 days.
Second method to solve this question ,
Here , x = 12 , y = 8 , z = 6Time taken = 2xyz - xy + yz + zx B alone can do in = 2 × 12 × 8 × 6 - 12 × 8 + 8 × 6 + 6 × 12 Time taken = 24 × 48 - 96 + 48 + 72 Time taken = 24 × 48 - 96 + 120 Time taken = 24 × 48 = 48 days. 24
- A and B can complete a piece of work in 30 days, B and C in 20 days, while C and A in 15 days. If all of them work together, the time taken in completing the work will be
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Work done by (A + B) in 1 day = 1 30 Work done by (B + C) in 1 day = 1 20 Work done by (C + A) in 1 day = 1 15
On adding,Work done by 2 (A +B + C) in 1 day = 1 + 1 + 1 30 20 15 Work done by 2 (A +B + C) in 1 day = 2 + 3 + 4 60 Work done by 2 (A +B + C) in 1 day = 9 = 3 60 20 ∴ Work done by (A + B + C) in 1day = 3 40 ∴ (A + B + C) will do the work in 40 = 13 1 days 3 3
Second method to solve this question ,
Here , x = 30 , y = 20 , z = 15
Correct Option: D
Work done by (A + B) in 1 day = 1 30 Work done by (B + C) in 1 day = 1 20 Work done by (C + A) in 1 day = 1 15
On adding,Work done by 2 (A +B + C) in 1 day = 1 + 1 + 1 30 20 15 Work done by 2 (A +B + C) in 1 day = 2 + 3 + 4 60 Work done by 2 (A +B + C) in 1 day = 9 = 3 60 20 ∴ Work done by (A + B + C) in 1day = 3 40 ∴ (A + B + C) will do the work in 40 = 13 1 days 3 3
Second method to solve this question ,
Here , x = 30 , y = 20 , z = 15Time taken = 2xyz xy + yz + zx Time taken = 2 × 30 × 20 × 15 30 × 20 + 20 × 15 + 15 × 30 Time taken = 18000 600 + 300 + 450 Time taken = 18000 = 13 1 days 1350 3
- A and B together can complete a work in 8 days and B and C to- gether in 12 days. All of the three together can complete the work in 6 days. In how much time will A and C together complete the work ?
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Let A and C complete the work in y days
(A + B)’s 1 day’s work = 1 8 (B + C)’s 1 day’s work = 1 12 (C + A)’s 1 day’s work = 1 y Then (A + B + B + C + C + A)’s 1 day’s work = 1 + 1 + 1 8 12 y 2(A + B + C)’s 1 day’s work = 3y + 2y + 24 24y (A + B + C)’s 1 day’s work = 5y + 24 24y × 2
According to the question,(A + B + C)’s 1 day’s work = 1 6 1 = 5y + 24 6 48y
⇒ 30y + 144 = 48y∴ = 144 = 8 days 18
Second method to solve this question ,
Here , p = 8 , q = 12 , r = yTime taken = 2pqr pq + qr + rp
Correct Option: A
Let A and C complete the work in y days
(A + B)’s 1 day’s work = 1 8 (B + C)’s 1 day’s work = 1 12 (C + A)’s 1 day’s work = 1 y Then (A + B + B + C + C + A)’s 1 day’s work = 1 + 1 + 1 8 12 y 2(A + B + C)’s 1 day’s work = 3y + 2y + 24 24y (A + B + C)’s 1 day’s work = 5y + 24 24y × 2
According to the question,(A + B + C)’s 1 day’s work = 1 6 1 = 5y + 24 6 48y
⇒ 30y + 144 = 48y∴ = 144 = 8 days 18
Second method to solve this question ,
Let the time taken by A and C be y days
Here , p = 8 , q = 12 , r = yTime taken = 2pqr pq + qr + rp ⇒ Total time taken = 2 × 8 × 12 × y 8 × 12 + 12 × y + 8 × y 6 = 192y 96 + 20y
⇒ 576 + 120y = 192y
⇒ 72y = 576
⇒ y = 8
Time taken by A and C is 8 days.
- A alone can complete a work in 12 days. A and B together can complete it in 8 days. How long will B alone take to complete the work ?
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A’s 1 day’s work = 1 12 (A+B)’s 1 day’s work = 1 8
∴ B’s 1 day’s work= 1 - 1 8 12 = 3 - 2 = 1 24 24
∴ B alone can do the work in 24 days.
Second method to solve this question ,
Here , x = 12 , y = 8Time taken by B = xy x - y Correct Option: A
A’s 1 day’s work = 1 12 (A+B)’s 1 day’s work = 1 8
∴ B’s 1 day’s work= 1 - 1 8 12 = 3 - 2 = 1 24 24
∴ B alone can do the work in 24 days.
Second method to solve this question ,
Here , x = 12 , y = 8Time taken by B = xy x - y Time taken by B = 12 × 8 = 24 days 12 - 8
