Time and Work
- A and B together can do a piece of work in 5 days and A alone can do it in 8 days. B alone can do the same piece of work in
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(A + B)’s 1 day’s work = 1 5 A’s 1 day’s work = 1 8 ∴ B’s 1 day’s work = 1 - 1 5 8 B’s 1 day’s work = 8 - 5 = 3 40 40 ∴ B alone will complete the work in 40 = 13 1 days 3 3
Second method to solve this question ,
Here , x = 5 , y = 8
Correct Option: C
(A + B)’s 1 day’s work = 1 5 A’s 1 day’s work = 1 8 ∴ B’s 1 day’s work = 1 - 1 5 8 B’s 1 day’s work = 8 - 5 = 3 40 40 ∴ B alone will complete the work in 40 = 13 1 days 3 3
Second method to solve this question ,
Here , x = 5 , y = 8
Time taken by B = 5 × 8 8 - 5 Time taken by B = 40 = 13 1 days 3 3
- A, B and C together can complete a piece of work in 30 minutes. A and B together can complete the same work in 50 minutes. C alone can complete the work in
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Work done by (A + B + C) in 1 minute = 1 30 Work done by (A + B) in 1 minute = 1 50 ∴ Work done by C alone in 1 minute = 1 - 1 30 50 Work done by C alone in 1 minute = 5 - 3 150 Work done by C alone in 1 minute = 2 = 1 150 75
∴ C alone will complete the work in 75 minutes.
Second method to solve this question ,
Here , x = 50 , y = 30
Correct Option: B
Work done by (A + B + C) in 1 minute = 1 30 Work done by (A + B) in 1 minute = 1 50 ∴ Work done by C alone in 1 minute = 1 - 1 30 50 Work done by C alone in 1 minute = 5 - 3 150 Work done by C alone in 1 minute = 2 = 1 150 75
∴ C alone will complete the work in 75 minutes.
Second method to solve this question ,
Here , x = 50 , y = 30C alone can do in = xy x - y
C alone can do in = 50 × 30 = 75 minutes 50 - 30
- A and B can do a piece of work in 8 days, B and C can do it in 24 days, while C and A
can do it in 8 7 days. In how many days can C do it alone? 4
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(A + B)’s 1 day’s work = 1 8 (B + C)’s 1 day’s work = 1 24
(C + A)’s 1 day’s work = 7 60
On adding all three,2 (A + B + C)’s 1 day’s work = 1 + 1 + 7 8 24 60 2 (A + B + C)’s 1 day’s work = 15 + 5 + 14 = 34 120 120 ∴ (A + B + C)’s 1 day’s work = 17 120 ∴ C’s 1 day’s work = 17 - 1 120 8 C’s 1 day’s work = 17 - 15 = 1 120 60
∴ C alone will complete the work in 60 days.
Second method to solve this question ,
Here , x = 8 , y = 24 , z = 60/7
C alone can do in = 2xyz xy - yz + zx
Correct Option: A
(A + B)’s 1 day’s work = 1 8 (B + C)’s 1 day’s work = 1 24
(C + A)’s 1 day’s work = 7 60
On adding all three,2 (A + B + C)’s 1 day’s work = 1 + 1 + 7 8 24 60 2 (A + B + C)’s 1 day’s work = 15 + 5 + 14 = 34 120 120 ∴ (A + B + C)’s 1 day’s work = 17 120 ∴ C’s 1 day’s work = 17 - 1 120 8 C’s 1 day’s work = 17 - 15 = 1 120 60
∴ C alone will complete the work in 60 days.
Second method to solve this question ,
Here , x = 8 , y = 24 , z = 60/7
C alone can do in = 2xyz xy - yz + zx C alone can do in = 2 × 8 × 24 × 60 7 8 × 24 - 24 × 60 + 60 × 8 7 7 C alone can do in = 23040 7 192 - 1440 + 480 7 7 C alone can do in = 23040 7 1344 - 1440 + 480 7 C alone can do in = 23040 × 7 = 60 days 7 384
- A and B can do a piece of work in 10 days. B and C can do it in 12 days. A and C can do it in 15 days. How long will A take to do it alone ?
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(A+B)’s 1 day’s work = 1 10 (B + C)’s 1 day’s work = 1 12 (C + A)’s 1 day’s work = 1 15
On adding all three,2(A + B + C)’s 1 day’s work = 1 + 1 + 1 10 12 15 2(A + B + C)’s 1 day’s work = 6 + 5 + 4 60 2(A + B + C)’s 1 day’s work = 15 = 1 60 4 ∴ (A + B + C)’s 1 day’s work = 1 8 ∴ A’s 1 day’s work = 1 - 1 8 12 A’s 1 day’s work = 3 - 2 = 1 24 24
∴ A will complete the work in 24 days.
Second method to solve this question ,
Here , x = 10 , y = 12 , z = 15A alone can do in = 2 × x × y × z xy + yz + zx
Correct Option: A
(A+B)’s 1 day’s work = 1 10 (B + C)’s 1 day’s work = 1 12 (C + A)’s 1 day’s work = 1 15
On adding all three,2(A + B + C)’s 1 day’s work = 1 + 1 + 1 10 12 15 2(A + B + C)’s 1 day’s work = 6 + 5 + 4 60 2(A + B + C)’s 1 day’s work = 15 = 1 60 4 ∴ (A + B + C)’s 1 day’s work = 1 8 ∴ A’s 1 day’s work = 1 - 1 8 12 A’s 1 day’s work = 3 - 2 = 1 24 24
∴ A will complete the work in 24 days.
Second method to solve this question ,
Here , x = 10 , y = 12 , z = 15A alone can do in = 2 × x × y × z xy + yz + zx A alone can do in = 2 × 10 × 12 × 15 10 × 12 + 12 × 15 - 15 × 10 A alone can do in = 3600 120 + 180 - 150 A alone can do in = 3600 = 24 days 150
- If A and B together can finish a piece of work in 20 days, B and C in 10 days and C and A in 12 days, then A, B, C jointly can finish the same work in
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(A + B)’s 1 day’s work = 1 20
(B + C)’s 1 day’s work = 1 10 (C + A)’s 1 day’s work = 1 12
On adding all three,2 (A + B + C)’s 1 day’s work = 1 + 1 + 1 20 10 12 2 (A + B + C)’s 1 day’s work = 3 + 6 + 5 60 2 (A + B + C)’s 1 day’s work = 14 = 7 60 30 ∴ (A + B + C)’s 1 day’s work = 7 60 ∴ Hence, the work will be completed in 60 = 8 4 days 7 7
Second method to solve this question ,
Here , x = 20 , y = 10 , z = 12Time taken = 2xyz xy + yz + zx
Correct Option: C
(A + B)’s 1 day’s work = 1 20
(B + C)’s 1 day’s work = 1 10 (C + A)’s 1 day’s work = 1 12
On adding all three,2 (A + B + C)’s 1 day’s work = 1 + 1 + 1 20 10 12 2 (A + B + C)’s 1 day’s work = 3 + 6 + 5 60 2 (A + B + C)’s 1 day’s work = 14 = 7 60 30 ∴ (A + B + C)’s 1 day’s work = 7 60 ∴ Hence, the work will be completed in 60 = 8 4 days 7 7
Second method to solve this question ,
Here , x = 20 , y = 10 , z = 12Time taken = 2xyz xy + yz + zx Time taken = 2 × 20 × 10 × 12 20 × 10 + 10 × 12 + 12 × 20 Time taken = 4800 200 + 120 + 240 Time taken = 4800 560 Time taken = 60 = 8 4 days 7 7
