Time and Work
- 15 men take 20 days to complete a job working 8 hours a day. The number of hours a day should 20 men take to complete the job in 12 days
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We can easily to solve this question with the help of given formula ,
M1 D1 T1 = M2 D2 T2
⇒ 15 × 20 × 8 = 20 × 12 × T2Correct Option: B
We can easily to solve this question with the help of given formula ,
M1 D1 T1 = M2 D2 T2
⇒ 15 × 20 × 8 = 20 × 12 × T2⇒ T2 = 15 × 20 × 8 = 10 hours 20 × 12
- Raj and Ram working together do a piece of work in 10 days. Raj alone can do it in 12 days. Ram alone will do the work in
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(Raj + Ram)’s 1 day’s work = 1 10 Raj’s 1 day’s work = 1 12 ∴ Ram’s 1 day’s work = 1 - 1 10 12 Ram’s 1 day’s work = 6 - 5 = 1 60 60
∴ Required time = 60 days
Second method to solve this question ,
Here , x = 12 , y = 10
Correct Option: D
(Raj + Ram)’s 1 day’s work = 1 10 Raj’s 1 day’s work = 1 12 ∴ Ram’s 1 day’s work = 1 - 1 10 12 Ram’s 1 day’s work = 6 - 5 = 1 60 60
∴ Required time = 60 days
Second method to solve this question ,
Here , x = 12 , y = 10Time taken = 10 × 12 = 60 days 12 - 10
- A and B can do a piece of work in 36 days, B and C can do it in 60 days, A and C can do it in 45 days. C alone can do it in
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(A + B)’s 1 day’s work = 1 36 (B + C)’s 1 day’s work = 1 60 (C + A)’s 1 day’s work = 1 45
Adding all three,2(A + B + C)’s 1 day’s work = 1 + 1 + 1 36 60 45 2(A + B + C)’s 1 day’s work = 5 + 3 +4 = 1 180 15 ∴ (A + B + C)’s 1 day’s work = 1 30 ∴ C’s 1 day’s work = 1 - 1 30 36 C’s 1 day’s work = 6 - 5 1 180 180
Hence, C alone will finish the work in 180 days.
Second method to solve this question ,
Here , x = 36 , y = 60 , z = 45
Correct Option: B
(A + B)’s 1 day’s work = 1 36 (B + C)’s 1 day’s work = 1 60 (C + A)’s 1 day’s work = 1 45
Adding all three,2(A + B + C)’s 1 day’s work = 1 + 1 + 1 36 60 45 2(A + B + C)’s 1 day’s work = 5 + 3 +4 = 1 180 15 ∴ (A + B + C)’s 1 day’s work = 1 30 ∴ C’s 1 day’s work = 1 - 1 30 36 C’s 1 day’s work = 6 - 5 1 180 180
Hence, C alone will finish the work in 180 days.
Second method to solve this question ,
Here , x = 36 , y = 60 , z = 45C alone can do in = 2xyz xy - yz + zx C alone can do in = 2 × 36 × 60 × 45 36 × 60 - 60 × 45 + 45 × 36 C alone can do in = 2 × 36 × 60 × 3 144 - 180 + 108 C alone can do in = 72 × 180 = 180 days 252 - 180
- How many men need to be employed to complete a job in 5 days, if 15 men can complete 1/3 of the job in 7 days ?
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we can solve this question with the help of given formula ,
15 men complete 1 work in 7 days. 3
∴ Time taken in doing 1 work
= 3 × 7 = 21 days
∴ M1 D1 = M2 D2
⇒ 15 × 21 = M2 × 5
Correct Option: D
we can solve this question with the help of given formula ,
15 men complete 1 work in 7 days. 3
∴ Time taken in doing 1 work
= 3 × 7 = 21 days
∴ M1 D1 = M2 D2
⇒ 15 × 21 = M2 × 5⇒ M2 = 15 × 21 = 63 days 5
- If x can finish a job in 4 hours and y can finish the same job in 8 hours independently, then they together will finish the job in
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(x and y)’s 1 hour work = 1 + 1 4 8 (x and y)’s 1 hour work = 2 + 1 = 3 8 8 ∴ Required time = 8 hours 3 Required time = 
8 × 60 
minutes = 160 minutes 3
Second method to solve this question ,
Here , x = 4 , y = 8
Correct Option: B
(x and y)’s 1 hour work = 1 + 1 4 8 (x and y)’s 1 hour work = 2 + 1 = 3 8 8 ∴ Required time = 8 hours 3 Required time = 8 × 60 minutes = 160 minutes 3
Second method to solve this question ,
Here , x = 4 , y = 8Time taken = xy hours x + y Time taken = 4 × 8 = 160 minutes 4 + 8
