Time and Work
- 4 mat-weavers can weave 4 mats in 4 days. At the same rate how many mats would be woven by 8 mat-weavers in 8 days ?
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Using Rule 1,
4 : 8 : : 4 : x 4 : 8
where, x is no. of mats
⇒ 4 × 4 × x = 8 × 8 × 4∴ x = 8 × 8 × 4 = 16 4 × 4 Correct Option: D
Using Rule 1,
4 : 8 : : 4 : x 4 : 8
where, x is no. of mats
⇒ 4 × 4 × x = 8 × 8 × 4∴ x = 8 × 8 × 4 = 16 4 × 4
- 5 persons can prepare an admission list in 8 days working 7 hours a day. If 2 persons join them so as to complete the work in 4 days, they need to work per day for :
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Using Rule 1,
More persons, less working hours/day
Less days, more working hours/dayPersons 7 : 5 : : 7 : x Days 4 : 8
where, x is hours/days
∴ 7 × 4 × x = 5 × 8 × 7∴ x = 5 × 8 × 7 = 10 hours 7 × 4 Correct Option: A
Using Rule 1,
More persons, less working hours/day
Less days, more working hours/dayPersons 7 : 5 : : 7 : x Days 4 : 8
where, x is hours/days
∴ 7 × 4 × x = 5 × 8 × 7∴ x = 5 × 8 × 7 = 10 hours 7 × 4
- A wall of 100 metres can be built by 7 men or 10 women in 10 days. How many days will 14 men and 20 women take to build a wall of 600 metres ?
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Using Rule 1,
7 men ≡ 10 womenor 1 man 10 women 7
14 men + 20 women= 10 × 14 + 20 women 7
= 40 women
Now, more work, more days
More women, less daysWork 1 : 6 : : 10 : x Women 40 : 10
Where x = number of days
⇒ 1 × 40 × x = 6 × 10 × 10or x = 600 = 15 40 Correct Option: A
Using Rule 1,
7 men ≡ 10 womenor 1 man 10 women 7
14 men + 20 women= 10 × 14 + 20 women 7
= 40 women
Now, more work, more days
More women, less daysWork 1 : 6 : : 10 : x Women 40 : 10
Where x = number of days
⇒ 1 × 40 × x = 6 × 10 × 10or x = 600 = 15 40
- If 72 men can build a wall of 280 m length in 21 days, how many men could take 18 days to build a similar type of wall of length 100 m?
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Using Rule 1,
We know thatW1 = W2 M1D1 M2D2 ⇒ 280 = 100 72 × 21 x × 18
Where x = number of men
⇒ x × 18 × 280 = 100 × 72 × 21⇒ x = 100 × 72 × 21 = 30 18 × 280 Correct Option: A
Using Rule 1,
We know thatW1 = W2 M1D1 M2D2 ⇒ 280 = 100 72 × 21 x × 18
Where x = number of men
⇒ x × 18 × 280 = 100 × 72 × 21⇒ x = 100 × 72 × 21 = 30 18 × 280
- 39 persons can repair a road in 12 days working 5 hours a day. In how many days will 30 persons working 6 hours a day complete the work ?
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Less persons, more days (Indirect)
More working hours/day, less days (Indirect)
Let required no. of days be x.∴ 30 : 39 : : 12 : x 6 : 5
⇒ 30 × 6 × x = 39 × 5 × 12⇒ x = 39 × 5 × 12 = 13 days 30 × 6
Aliter : Using Rule 1,
Here, M1 = 39, D1 = 12, T1 = 5
M2 = 30, D2 = ?, T2 = 6
M1D1T1 = M2D2T2
39 × 12 × 5 = 30 × D2 × 6⇒ D2 = 39 × 12 × 5 = 13 days 30 × 6 Correct Option: B
Less persons, more days (Indirect)
More working hours/day, less days (Indirect)
Let required no. of days be x.∴ 30 : 39 : : 12 : x 6 : 5
⇒ 30 × 6 × x = 39 × 5 × 12⇒ x = 39 × 5 × 12 = 13 days 30 × 6
Aliter : Using Rule 1,
Here, M1 = 39, D1 = 12, T1 = 5
M2 = 30, D2 = ?, T2 = 6
M1D1T1 = M2D2T2
39 × 12 × 5 = 30 × D2 × 6⇒ D2 = 39 × 12 × 5 = 13 days 30 × 6