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
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
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
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
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
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)
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)
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
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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