Time and Work
- A piece of work was to be completed in 40 days, a number of men employed upon it did only half the work in 24 days, 16 more men were then set on and the work was completed in the specified time, how many men were employed at first ?
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Let N men were employed at first
∵ N men do 1/2 of the work in 24 days
∴ 1 man do the whole work in 24 x 2 x N = 48N days
Now, from the question,
(N + 16) men do the remaining work (1 - 1/2) = 1/2 in (40 - 24) = 16 daysCorrect Option: B
Let N men were employed at first
∵ N men do 1/2 of the work in 24 days
∴ 1 man do the whole work in 24 x 2 x N = 48N days
Now, from the question,
(N + 16) men do the remaining work (1 - 1/2) = 1/2 in (40 - 24) = 16 days
∴ 1 man do the whole work in 16 x 2 x (N + 16) days
∴ 48N = 32(N + 16)
∴ N = 32 men
- If 5 men and 3 boys can reap 23 hectares in 4 days and if 3 men and two boys can reap 7 hectares in 2 days. How many boys must assist 7 men in order that they may reap 45 hectares in 6 days ?
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5 men + 3 boys can reap 23 hectares in 4 days ......(i)
3 men + 2 boys can reap 7 hectares in 2 days ......(ii)
∴ From (i),
14( 5 men + 3 boys) can reap 23 x 14 hectares in 4 days
Now, from (ii)
⇒ 23 (3 men + 2 boys) can reap 7 x 2 x 23 hectares in 4 days
∵ 14(5 men + 3 boys) = 23 (3 men + 2 boys)
⇒ 70 men + 42 boys = 69 men + 46 boys
∴ 1 men = 4 boysCorrect Option: A
5 men + 3 boys can reap 23 hectares in 4 days ......(i)
3 men + 2 boys can reap 7 hectares in 2 days ......(ii)
∴ From (i),
14( 5 men + 3 boys) can reap 23 x 14 hectares in 4 days
Now, from (ii)
⇒ 23 (3 men + 2 boys) can reap 7 x 2 x 23 hectares in 4 days
∵ 14(5 men + 3 boys) = 23 (3 men + 2 boys)
⇒ 70 men + 42 boys = 69 men + 46 boys
∴ 1 men = 4 boys
Now, 5 men + 3 boys = 23 boys
⇒ 23 boys can reap 23 hectare 4 days
⇒ 1 boy can reap 1 hectares in 4 days
⇒ 4 boys can reap 1 hectare in 1 day
⇒ 4 x 45 boys can reap 45 hectaes in 1 day
⇒ 4 x 45 / 6 boys can reap 45 hectares in 6 days
∴ 30 boys can reap 45 hectares in 6 days
But 30 boys = 28 boys + 2 boys = 7 men + 2 boys
Hence, 2 boys can assist 7 men for the work.
- 14 persons can complete a work in 16 days. 8 persons started the work 12 days after they started the work 8 more person joined them. How many days will they take to complete the remaining work ?
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∵ 14 person complete in 16 days = 1 work
∴ 8 person complete in 12 days = 1 x (8/14) x (12/16) = 3/7
∴ Remaining work = 1 - 3/7 = 4/7
and total number of person = 8 + 8 = 16
∴ 14 person do 1 work in 16 days
∴ 16 person do 4/7 work in 16 x (14/16) x (4/7) = 8 daysCorrect Option: D
∵ 14 person complete in 16 days = 1 work
∴ 8 person complete in 12 days = 1 x (8/14) x (12/16) = 3/7
∴ Remaining work = 1 - 3/7 = 4/7
and total number of person = 8 + 8 = 16
∴ 14 person do 1 work in 16 days
∴ 16 person do 4/7 work in 16 x (14/16) x (4/7) = 8 days
- Typist A can type a report in 16 hours. Typist B can type the same report in 20 hours and the typist C in 24 hours. All the three typist started typing at 9.00 a.m. at 1.00 p.m. the typist A stopped typing. The other two typists finished the job. Approximately at what time the report was typed ?
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Work of (A + B + C) for 1 hour = 1/16 + 1/20 + 1/24 = 37/240
∴ Work of (A + B + C) for 4 hours = 4 x 37/240 = 37/60
∴ Remaining work = 1 - 37/60 = 23/60
∴ Work of (B + C) for 1 hour = 1/20 + 1/24 = 11/120
∵ 11/120 work is done by (B + C) in 1 hour
∴ 23/60 work is done by (B + C) = 120/11 x 23/60 = 46/11 hours = 4 hours 11 min.
∴ The type at which the report was typed = 01 : 00 + 04 : 11 = 05 : 11 p.m.Correct Option: B
Work of (A + B + C) for 1 hour = 1/16 + 1/20 + 1/24 = 37/240
∴ Work of (A + B + C) for 4 hours = 4 x 37/240 = 37/60
∴ Remaining work = 1 - 37/60 = 23/60
∴ Work of (B + C) for 1 hour = 1/20 + 1/24 = 11/120
∵ 11/120 work is done by (B + C) in 1 hour
∴ 23/60 work is done by (B + C) = 120/11 x 23/60 = 46/11 hours = 4 hours 11 min.
∴ The type at which the report was typed = 01 : 00 + 04 : 11 = 05 : 11 p.m.
- A contractor undertook to do a piece of work in 9 days. He employed a certain number of laborious but 6 of them being absent from the very first day, the rest could finish the work in 15 days. Find the number of men originally employed.
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Let the number of men originally employed = x
So, (x - 6) men could finish the work in 15 days and x men could finish the work in 9 days.
∴ 9x = 15(x - 6)Correct Option: A
Let the number of men originally employed = x
So, (x - 6) men could finish the work in 15 days and x men could finish the work in 9 days.
∴ 9x = 15(x - 6)
⇒ x = 15
