# Time and Work - Aptitude Questions and Answers - RejinpaulPlacement

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8.
A and B undertake to do a piece of work for Rs.600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of each.

Solution:   C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/24.

A : B : C = Ratio of their 1 day's work = 1/6 : 1/8 : 1/24 = 4 : 3 : 1

A's share = Rs. [600 * (4/8)] = Rs. 300
B's share = Rs. [600 * (3/8)] = Rs. 225
C's share = Rs. [600 - (300 + 225)] = Rs. 75
9.
A and B working separately can do a piece of work in 9 days and 12 days respectively. If they work for a work alternately, A beginning, in how many days, the work will be completed?

Solution:   (A + B)'s 2 day's work = (1/9 + 1/12) = 7/36
Work done in 5 pairs of days = [5 * (7/36)] = 35/36

Remaining work = [1 - (35/36)] = 1/36
On 11th day, it is A's turn.
1/9 work is done by him in 1 day.

1/36 work is done by him in [9 * (1/36)] = 1/4 days.

Total time taken = [10 + (1/4 )] days = 10   1/4 days
10.
45 men can complete a work in 16 days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining work?

Solution:   (45 * 16) men can complete the work in 1 day.

1 man's 1 day's work = 1/720
45 men's 6 day's work = [(1/16) * 6] = 3/8
Remaining work = [1 - 3/8] = 5/8

75 men's 1 day's work = 75/720 = 5/48
Now, 5/48 work is done by them in 1 day.

5/8 work is done by them in [(48/5) * (5/8)] = 6 days.
11.
2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work?

Solution:   Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y
Then, 2x + 3y = 1/10 and 3x + 2y = 1/8

Solving, we get: x = 7/200 and y = 1/100

(2 man + 1 boy)'s 1 day's work = [2 * (7/200) + 1 * (1/100)] = 16/200 = 2/25

So, 2 men and 1 boy together can finish the work in 25/2 = 12   1/2 days.
12.
A does a work in 10 days and B does the same work in 15 days. In how many days they together will do the same work? [R.R.B. 2003]

Solution:  A's 1 day's work = 1/10 and B's 1 day's work = 1/15

(A + B)'s 1 day's work = (1/10 + 1/15) = 1/6

So, both together will finish the work in 6 days.
13.
A an finish a work in 18 days and B can do the same work in half the time taken by A. Then, working together, what part of the same work they can finish in a day? [S.S.C 2002]