Time and Work
- A and B together can do a piece of work in 10 days. A alone can do it in 30 days. The time in which B alone can do it is
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(A + B)’s 1 day’s work = 1 10 A’s 1 day’s work = 1 30 ∴ B’s 1 day’s work = 1 - 1 10 30 B’s 1 day’s work = 3 - 1 = 2 = 1 30 30 15
Hence, B, alone can complete the work in 15 days.
Second method to solve this question ,
Here , x = 30 , y = 10
Correct Option: C
(A + B)’s 1 day’s work = 1 10 A’s 1 day’s work = 1 30 ∴ B’s 1 day’s work = 1 - 1 10 30 B’s 1 day’s work = 3 - 1 = 2 = 1 30 30 15
Hence, B, alone can complete the work in 15 days.
Second method to solve this question ,
Here , x = 30 , y = 10Time taken by B = xy x - y Time taken by B = 30 × 10 = 15 days 30 - 10
- A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in
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A’s 1 day’s work = 1 24
B’s 1 day’s work = 1 6 C’s 1 day’s work = 1 12 (A + B + C)’s 1 day’s work = 1 + 1 + 1 24 6 12 (A + B + C)’s 1 day’s work = 1 + 4 + 2 = 7 24 24 ∴ The work will be completed by them in 24 i.e., 3 3 days 7 7
Second method to solve this question ,
Here , x = 24 , y = 6 , z = 12
Correct Option: C
A’s 1 day’s work = 1 24
B’s 1 day’s work = 1 6 C’s 1 day’s work = 1 12 (A + B + C)’s 1 day’s work = 1 + 1 + 1 24 6 12 (A + B + C)’s 1 day’s work = 1 + 4 + 2 = 7 24 24 ∴ The work will be completed by them in 24 i.e., 3 3 days 7 7
Second method to solve this question ,
Here , x = 24 , y = 6 , z = 12Time taken = 24 × 6 × 12 24 × 6 + 6 × 12 + 24 × 12 Time taken = 1728 144 + 72 + 288 Time taken = 1728 = 24 504 7 Time taken = 3 3 days 7
- A can do a piece of work in 4 hours; B and C can do it in 3 hours. A and C can do it in 2 hours. How long will B alone take to do it ?
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A’s 1 hour’s work = 1 4 (B + C)’s 1 hour’s work = 1 3 (A + C)’s 1 hour’s work = 1 2 ∴ C’s 1 hour’s work = 1 - 1 2 4 C’s 1 hour’s work = 2- 1 = 1 4 4
Correct Option: B
A’s 1 hour’s work = 1 4 (B + C)’s 1 hour’s work = 1 3 (A + C)’s 1 hour’s work = 1 2 ∴ C’s 1 hour’s work = 1 - 1 2 4 C’s 1 hour’s work = 2- 1 = 1 4 4 and B’s 1 hour’s work = 1 - 1 3 4 B’s 1 hour’s work = 4 - 3 = 1 12 12
Hence, B alone can do the work in 12 hours.
- A and B can do a piece of work in 10 days, B and C in 15 days and C and A in 20 days. C alone can do the work in :
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According to the question ,
Work done by A and B together in one day = 1 part 10 Work done by B and C together in one day = 1 part 15 Work done by C and A together in one day = 1 part 20
So,A + B = 1 ....(I) 10 B + C = 1 ....(II) 15 C + A = 1 ....(III) 20
Adding I, II, III, we get2 (A + B + C) = 1 + 1 + 1 10 15 20 2 (A + B + C) = 6 + 4 + 3 = 13 60 60 A + B + C = 13 ....(IV) 120
Putting the value of eqn. (I) in eqn. (IV)1 + C = 13 10 120 C = 13 - 1 120 10 C = 13 - 12 = 1 120 120 ∴ Work done in 1 day by C is 1 Part 120
Hence, C will finish the whole work in 120 days
Second method to solve this question ,
Here , x = 10 , y = 15 , z = 20
Correct Option: B
According to the question ,
Work done by A and B together in one day = 1 part 10 Work done by B and C together in one day = 1 part 15 Work done by C and A together in one day = 1 part 20
So,A + B = 1 ....(I) 10 B + C = 1 ....(II) 15 C + A = 1 ....(III) 20
Adding I, II, III, we get2 (A + B + C) = 1 + 1 + 1 10 15 20 2 (A + B + C) = 6 + 4 + 3 = 13 60 60 A + B + C = 13 ....(IV) 120
Putting the value of eqn. (I) in eqn. (IV)1 + C = 13 10 120 C = 13 - 1 120 10 C = 13 - 12 = 1 120 120 ∴ Work done in 1 day by C is 1 Part 120
Hence, C will finish the whole work in 120 days
Second method to solve this question ,
Here , x = 10 , y = 15 , z = 20Time Taken by C = 2xyz xy - yz + zx Time Taken by C = 2 × 10 × 15 × 20 10 × 15 - 15 × 20 + 20 × 10 Time Taken by C = 6000 150 - 300 + 200 Time Taken by C = 6000 = 120 days 50
- A can do a work in 6 days and B in 9 days. How many days will both take together to complete the work?
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According to question,
A can finish the whole work in 6 days.∴ A’s one day’s work = 1 6
Similarly,
B’s one day’s work = 1 9 (A + B)’s one day’s work = 
1 + 1 
= 3 + 2 6 9 18 (A + B)’s one day’s work = 5 18 Therefore, (A + B)’s can finish the whole work in = 18 days i.e, 3.6 days. 5
Second method to solve this question ,
Here , x = 6 , y = 9
Correct Option: C
According to question,
A can finish the whole work in 6 days.∴ A’s one day’s work = 1 6
Similarly,
B’s one day’s work = 1 9 (A + B)’s one day’s work = 1 + 1 = 3 + 2 6 9 18 (A + B)’s one day’s work = 5 18 Therefore, (A + B)’s can finish the whole work in = 18 days i.e, 3.6 days. 5
Second method to solve this question ,
Here , x = 6 , y = 9Time taken = 2xy x+ y Time taken = 6 × 9 = 54 = 3.6 days 9 + 6 15
