Time and Work
- 3 men and 7 women can do a job in 5 days, while 4 men and 6 women can do it in 4 days. The number of days required for a group of 10 women working together, at the same rate as before, to finish the same job is :
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3 × 5 men + 7 × 5 women
= 4 × 4 men + 6 × 4 women
⇒ 16 men – 15 men = 35 women – 24 women
∴ 1 man = 11 women
⇒ 3 men + 7 women = 40 women
∴ M1D1 = M2D2
⇒ 40 × 5 = 10 × D2
⇒ D2 = 20 days
Aliter : Using Rule 11,
Here, A1 = 3, B1 = 7, D1 = 5
A2 = 4, B2 = 6, D2 = 4
A3 = 0, B3 = 10
Required days= D1D2(A1B2 - A2B1) days D1(A1B3 - A3B1) - D2(A2B3 - A3B2) = 5 × 4(3 × 6 - 4 × 7) 5(3 × 10 - 0) - 4(4 × 10 - 0) = 20 × (-10) = 20 days 150 - 160 Correct Option: D
3 × 5 men + 7 × 5 women
= 4 × 4 men + 6 × 4 women
⇒ 16 men – 15 men = 35 women – 24 women
∴ 1 man = 11 women
⇒ 3 men + 7 women = 40 women
∴ M1D1 = M2D2
⇒ 40 × 5 = 10 × D2
⇒ D2 = 20 days
Aliter : Using Rule 11,
Here, A1 = 3, B1 = 7, D1 = 5
A2 = 4, B2 = 6, D2 = 4
A3 = 0, B3 = 10
Required days= D1D2(A1B2 - A2B1) days D1(A1B3 - A3B1) - D2(A2B3 - A3B2) = 5 × 4(3 × 6 - 4 × 7) 5(3 × 10 - 0) - 4(4 × 10 - 0) = 20 × (-10) = 20 days 150 - 160
- Some persons can do a piece of work in 12 days. Two times the number of such persons will do half of the work in
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Using Rule 1,
M1D1 = M2D2 W1 W2 ⇒ M × 12 = 2M × D2 W W 2 M × 12 = 4M × D2 W W
⇒ D2 = 3 daysCorrect Option: D
Using Rule 1,
M1D1 = M2D2 W1 W2 ⇒ M × 12 = 2M × D2 W W 2 M × 12 = 4M × D2 W W
⇒ D2 = 3 days
- If the work done by (x –1) men in (x + 1) days is to the work done by (x + 2) men in (x – 1) days are in the ratio 9 : 10, then the value of x is equal to :
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Using Rule 1,
M1D1 = M2D2 W1 W2 ∴ W1 = M1D1 W2 M2D2 ∴ 9 = (x - 1)(x + 1) = x + 1 10 (x + 2)(x - 1) x + 2
⇒ 10x + 10 = 9x + 18
⇒ x = 18 – 10 = 8Correct Option: D
Using Rule 1,
M1D1 = M2D2 W1 W2 ∴ W1 = M1D1 W2 M2D2 ∴ 9 = (x - 1)(x + 1) = x + 1 10 (x + 2)(x - 1) x + 2
⇒ 10x + 10 = 9x + 18
⇒ x = 18 – 10 = 8
- If 80 persons can finish a work within 16 days by working 6 hours a day, the number of hours a day, should 64 persons work to finish that very job within 15 days is :
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Using Rule 1,
M1D1T1 = M2D2T2
⇒ 80 × 16 × 6 = 64 × 15 × T2⇒ T2 = 80 × 16 × 6 = 8 hours 64 × 15 Correct Option: C
Using Rule 1,
M1D1T1 = M2D2T2
⇒ 80 × 16 × 6 = 64 × 15 × T2⇒ T2 = 80 × 16 × 6 = 8 hours 64 × 15
- 18 boys can do a piece of work in 24 days. In how many days can 27 boys do the same work ?
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View Hint View Answer Discuss in Forum
Using Rule 1,
M1D1 = M2D2
⇒ 18 × 24 = 27 × D2⇒ D2 = 18 × 24 = 16 days 27 Correct Option: A
Using Rule 1,
M1D1 = M2D2
⇒ 18 × 24 = 27 × D2⇒ D2 = 18 × 24 = 16 days 27
