Time and Work
- 3 men can do a piece of work in 18 days. 6 children can also do that work in 18 days. 4 men and 4 children together will finish the work in how many days ?
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3 men = 6 children
⇒ 1 man = 2 children
∴ 4 men + 4 children = 4 men + (4/2) men = 6 men
Given, M1 = 3, M2 = 6, D1 = 18, W1 = W2 = 1 and D2= ?
According to the formula,
M1D1W2 = M2D2W1Correct Option: D
3 men = 6 children
⇒ 1 man = 2 children
∴ 4 men + 4 children = 4 men + (4/2) men = 6 men
Given, M1 = 3, M2 = 6, D1 = 18, W1 = W2 = 1 and D2= ?
According to the formula,
M1D1W2 = M2D2W1
⇒ 3 x 18 x 1 = 6 x D2 x 1
∴ D2 = 3 x 18/6 = 9 days
- 3 men can do a piece of work in 6 days. 5 women can do the same work in 18 days. If 4 men and 10 women work together, then how long will it take to finish the work ?
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(3 x 6) men = (5 x 18) women
18 men = 90 women
∴ 1 man = 5 women
∴ 4 men + 10 women
= 4 x 5 + 10 = 30 women
Given, M1 = 5, M2 = 20, D1 = 18 ,
W1 = W2 = 1 and D2 = ?
According to the formula, M1D1W2 = M2D2W1Correct Option: A
(3 x 6) men = (5 x 18) women
18 men = 90 women
∴ 1 man = 5 women
∴ 4 men + 10 women
= 4 x 5 + 10 = 30 women
Given, M1 = 5, M2 = 20, D1 = 18 ,
W1 = W2 = 1 and D2 = ?
According to the formula, M1D1W2 = M2D2W1
⇒ 5 x 18 x 1 = 30 x D2 x 1
∴ D2 = 5 x 18/30 = 3 days
- 10 men can make a wall in 8 days. How many men required to complete the same work in half days ?
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Given M1 = 10
D1 = 8, M2= ? and D2 = 1/2
From M1 D1 = M2 D2Correct Option: D
Given M1 = 10
D1 = 8, M2= ? and D2 = 1/2
From M1 D1 = M2 D2
⇒ 10 x 8 = M2 x 1/2
⇒ M2= 10 x 8 x 2
∴ M2 = 160
- X can completed a job in 12 days. If X and Y work together, they can complete the job in 62/3 days, Y alone can complete the job in
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X's 1 day's work = 1/12
(X + Y)' s 1 day's work = 3/20
∴ Y's 1 day's work = (3/20) - (1/12) = 4/60 = 1/15Correct Option: C
X's 1 day's work = 1/12
(X + Y)' s 1 day's work = 3/20
∴ Y's 1 day's work = (3/20) - (1/12) = 4/60 = 1/15
∴ Number of day's taken by Y to complete the work = 15 days
- A and B together can do a work in 10 days. B and C together can do the same work in 6 days. A and C together can do the work in 12 days. Then A, B and C together can do the work in
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(A + B)’s 1 day’s work = 1 10
(B + C)’s 1 day’s work = 1 6
(C + A)’s 1 day’s work = 1 12
Adding all three ,2 (A + B + C)’s 1 day’s work = 1 + 1 + 1 10 6 12 2 (A + B + C)’s 1 day’s work = 6 + 10 + 5 60 2 (A + B + C)’s 1 day’s work = 21 = 7 60 20 ∴ (A + B + C)’s 1 day’s work = 7 40 ∴ All three together will complete the work in = 40 = 5 5 7 7
Second method to solve this question ,
Here , x = 10 , y = 6 , z = 12
Correct Option: C
(A + B)’s 1 day’s work = 1 10
(B + C)’s 1 day’s work = 1 6
(C + A)’s 1 day’s work = 1 12
Adding all three ,2 (A + B + C)’s 1 day’s work = 1 + 1 + 1 10 6 12 2 (A + B + C)’s 1 day’s work = 6 + 10 + 5 60 2 (A + B + C)’s 1 day’s work = 21 = 7 60 20 ∴ (A + B + C)’s 1 day’s work = 7 40 ∴ All three together will complete the work in = 40 = 5 5 7 7
Second method to solve this question ,
Here , x = 10 , y = 6 , z = 12Time taken = 2 × 10 × 6 × 12 = 1440 10 × 6 + 6 × 12 + 12 × 10 60 + 72 + 120 Time taken = 1440 = 40 252 7 Time taken = 5 5 days 7
