Aptitude Time And WorkPage 5
33. | | A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was? | | (a)6 | | (b)8 | | (c)9 | | (d)12 |
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Answer is: C(A + B)'s 1 day's work = (1/45 + 1/40) = 17/360.
Work done by B in 23 days = 1/40 X 23 = 23/40.
Remaining work = (1 - 23/40) = 17/40.
Now, 17/360 work was done by (A + B) in 1 day.
17/40 work was done by (A + B) in 1 X (360/17) X (17/40) = 9 days.
Hence, A left after 9 days.
34. | | Rohan can do a work in 3 days while Sohan can do the same work in 2 days. Both of them finish the work together and get Rs. 150. What is the share of Rohan? | | (a)Rs. 30 | | (b)Rs. 60 | | (c)Rs. 70 | | (d)Rs. 75 |
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Answer is: BRohan's wages : Sohan's wages = Rohan's 1 day's work : Sohan's 1 day's work. = 1/3 : 1/2 = 2 : 3
Hence, Rohan's share = Rs. 2/5 X 180 = Rs. 60.
35. | | A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work? | | (a)10 days | | (b)11 days | | (c)15 days | | (d)20 days |
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Answer is: CB's 1 day's work = (1/12 - 1/20) = 1/30.
Now, (A + B)'s 1 day's work = (1/20 + 1/60) = 4/60 = 1/15. ( B works for half day only)
So, A and B together complete the work in 15 days.
36. | | A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? | | (a)12 days | | (b)15 days | | (c)16 days | | (d)18 days |
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Answer is: BA's 2 day's work = (1/20) X 2 = 1/10.
(A + B + C)'s 1 day's work = (1/20 + 1/30 + 1/60) = 6/60 = 1/10.
Work done in 3 days = (1/10 + 1/10) = 1/5
Now, 1/5 work is done in 3 days.
Hence, whole work will be done in ( 3 x 5) = 15 days.
37. | | 12 men complete a work in 9 days. After they have worked for 6 days, 6 more men join them. How many days will they take to complete the remaining work? | | (a)2 days | | (b)3 days | | (c)4 days | | (d)5 days |
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Answer is: A1 man's 1 day's work = 1/108
12 men's 6 day's work = (1/9) X 6 = 2/3.
Remaining work = (1 - 2/3) = 1/3.
18 men's 1 day's work = (1/108) X 18 = 1/6
1/6 work is done by them in 1 day.
Hence, 1/3 work is done by them in (6 x 1/3) = 2 days.
38. | | 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work? | | (a)3 | | (b)5 | | (c)7 | | (d)cannot be determined (cbd) |
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Answer is: C1 woman's 1 day's work = 1/70
1 child's work = 1/140
(5 women + 10 children)'s 1 day's work = (5/70 + 10/140) = (1/14 + 1/14) = 1/7.
5 women and 10 children will complete the work in 7 days.
39. | | Three men, four women and six children can complete a work in seven days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days? | | (a)7 | | (b)8 | | (c)12 | | (d)cannot be determined (cbd) |
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Answer is: ALet 1 woman's 1 day's work = x.
Then, 1 men's 1 day's work = x/2 and 1 child's 1 day's work = x/4.
So, (3x/2 + 4x + 6x/4) = 1/7
28x/4 = 1/7
x = 1/49.
1 woman alone can complete the work in 49 days.
So, to complete the work in 7 days, number of women required = (49/7) = 7.
40. | | 10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work? | | (a)90 | | (b)125 | | (c)145 | | (d)None of these |
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Answer is: D1 men's 1 day's work = 1/100.
(10 men + 15 women)'s 1 day's work = 1/6.
15 women's 1 day's work = (1/6 - 10/100) = 1/15.
1 woman's 1 day's work = 1/225.
1 women alone can complete the work in 225 days
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