## Aptitude Time And WorkPage 1

1. If A can do a piece of work in n days, then A's 1 day's work = 1/n
2. If A's 1 day's work = 1/n, then A can finish the work in n days
3. If A is thrice as good as in work B, then:
Ratio of work done by A and B = 3 : 1.
Ratio of time taken by A and B to finish a work = 1 : 3.

4. Short Tricks

If M1 can do a W1 work in D1 days working H1 hour per day
and M2 can do a W2 work in D2 days working H2 hour per day, Then

M1D1W2 = M2D2W1
M1D1T1W2 = M2D2T2W1 (When time is given)
M1D1T1E1W2 = M2D2T2E2W1 (When efficiency is added)

M = Person
D = Days
W = Work
T = Time
E = Efficiency

1.

 A and B can do a project in 20 days and 30 respectively. They were told to complete the project in 8 days and were paid in 1170 rupees. They took the help of C and completed the work in time. Find C's share in the total money earned by them? (a)200 (b)330 (c)390 (d)360
Answer is: CA and B can do (1/20)th and (1/30)th part of total work in a day respectively.
in 8 days they can do 8(1/20 + 1/30) = 8/12 = (2/3)rd of the total work.
So, C has to do (1/3)rd of total work.
his share is (1/3)rd of total money. i.e. (1/3) X 1170 = 390

2.

 Ajay can do a certain work in 16 days. He start the work, works for 4 days and then quits. Bharat takes up the job and does the remaining work. If Bharat alone takes 24 days to do the entire work, in total how many days will the work be completed? (a)22 (b)24 (c)20 (d)26
Answer is: AAjay can do the work in 16 days.
so , ajay's one day's work = (1/16)th of the work.
in 4 days he can do (4 X 1)/16 = (1/4)th of the work.
Bharat has to do 1 - (1/4) = 3/4 of the work.
so, To do 3/4th of the work he takes (3/4) X 24 = 18 days.
Total days = 4 +18 = 22 days

3.

 P and Q can do certain work in 28 days and 56 days respectively. P work for 7 days, and then Q joins P. In how many more days can they complete the work? (a)7 days (b)14 days (c)21 days (d)28 days
Answer is: BP can do (1/28)th of the work in a day i.e. in 7 days he completes (1/28) X 7 = (1/4)th of the work.
the remaining part of work (i.e. 3/4 of the work) is completed by P and Q working together at rate of (1/28 + 1/56) = 3/56 of the par day.
so , they take (3/4) X (56/3) = 14 days more to complete remaining work together.

4.

 P can do a certain work in 4 days and Q can do the same work in 12 days. They work together for a few days after P leaves and Q alone completes the remaining work. If it takes 6 days to complete the entire work, after how many days does P quit? (a)3 days (b)4 days (c)2 days (d)5 days
Answer is: CP can do (1/4)th the work in 1 day and Q can do (1/12)th of the work in 1 day.
if they work for x days together,they complete x{1/4 + 1/12}th of work i.e. (x/3)rd of work.
So, {1 - x/3} work is done by Q alone.
He completes this work in {(3 - x)/3 X 12} = (12 - 4x) days.
Total no. of days taken x + (12 - 4x) = 6 days.
So, x = 2 days, P quits after 2 days.

5.

 A can do a work in 6 days, which B can do in 9 days and C can do in 12 days. If a similar work is done in 24 days by all three of them working together, how many days will B alone take to complete that work? (a)68 days (b)48 days (c)54 days (d)78 days
Answer is: DInitially let the amount of work be x units which A, B, C do in 6, 9,12 days respectively.
A does x/6 units of work in a day.
B does x/9 units of work in a day.
C does x/12 units of work in a day.
So, they can do {x/6 + x/9 + x/12} units of work by working together in 1 day.
In 24 days the amount of work done = 24 X (13x/36) = 26x/3 units.
B can do 26x/3 units of work done by in 26x X 9/3x = 78 days.
B can complete in 78 days.

6.

 A group of 5 people can do a certain work in a certain number of days. If 4 more people join the group, they take 12 days less to do the same work. in how many days a group of 3 people can do the work? (a)30 days (b)45 days (c)15 days (d)60
Answer is: BLet 5 people do the work in x days. Then 9 people will do the work in (x - 12) days.
But, work done by both sets of people is the same
So, 5 X x = 9(x - 12)
5x = 9x - 108
x = 27 days
If 3 people take y days, then 5 X 27 = 3 X y
y = 45 days.

7.

 B takes 18 days more than A to do a work. If A is thrice as efficient as B, and if they work together, in how many days do they complete the work? (a)6 days (b)7 days (c)31/4 days (d)27/4 days
Answer is: DLet, A takes x days for complete work then B takes (x + 18) days for complete work.
A is thrice more efficient than B.
So, M1D1 = M2D2
3 X x = 1 X (x + 18)
2x = 18
x = 9
A takes 9 days and B takes (9 + 18) days.
They work together = 1/9 + 1/18 = 4/27
They finish work 27/4 days.

8.

 P and Q can do a certain piece of work in 10 and 15 days respectively. P and Q work for 3 days each alternately till the work is completed. If P start the work, in how many days will the work be completed? (a)6 (b)9 (c)18 (d)12
Answer is: DP and Q can do (1/10)th and (1/15)th of the total work in la day respectively.
In 6 days, they do (3/10 + 3/15)th of the total work i.e. (1/2) of the total work.
So, they complete the work in 12 days

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