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Q:

# A and B can do a piece of work in 40 and 50 days. If they work at it an alternate days with A beginning in how many days, the work will be finished ?

Q:

A garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement ?

 A) 1900 B) 2100 C) 1700 D) 2000

Explanation:

Given 2000 ---- 54

The provisions for 2000 men for 39 days can be completed by 'm' men for only 20 days.

i.e, 2000 ----- 39 days == m ---- 20 days
=> m x 20 = 2000 x 39
m = 3900
So total men for 20 days is 3900 => 2000 old and 1900 new reinforcement.

Hence, reinforcement = 1900.

1 14
Q:

A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in ?

 A) 3 hrs B) 6 hrs C) 7 hrs D) 5 hrs

Explanation:

Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/2
6/x = 1/2 => x = 12
So, B takes 6 hours to finish the work.

2 35
Q:

A can complete a work in 12 days with a working of 8 hours per day. B can complete the same work in 8 days when working 10 hours a day. If A and B work together, working 8 hours a day, the work can be completed in --- days  ?

 A) 51/24 B) 87/5 C) 57/12 D) 60/11

Explanation:

A can complete the work in 12 days working 8 hours a day

=> Number of hours A can complete the work = 12×8 = 96 hours

=> Work done by A in 1 hour = 1/96

B can complete the work in 8 days working 10 hours a day

=> Number of hours B can complete the work = 8×10 = 80 hours

=> Work done by B in 1 hour = 1/80

Work done by A and B in 1 hour = 1/96 + 1/80 = 11/480

=> A and B can complete the work in 480/11 hours

A and B works 8 hours a day

Hence total days to complete the work with A and B working together

= (480/11)/ (8) = 60/11 days

4 47
Q:

K can build a wall in 30 days. L can demolish that wall in 60 days. If K and L work on alternate days, when will the wall be completed ?

 A) 120 days B) 119 days C) 118 days D) 117 days

Explanation:

K's work in a day(1st day) = 1/30
L's work in a day(2nd day)= -1/60(demolishing)
hence in 2 days, combined work= 1/30 - 1/60
=1/60
since both works alternatively, K will work in odd days and L will work in even days.
1/60 unit work is done in 2 days
58/60 unit work will be done in 2 x 58 days = 116 days
Remaining work = 1-58/60
= 2/60
= 1/30
Next day, it will be K's turn and K will finish the remaining 1/30 work.
hence total days = 116 + 1 = 117.

5 101
Q:

A contractor undertook to complete a piece of work in 120 Days and employed 140 men upon it. At the end of 66 days only half of the work was done,so he put on 25 extra men. By how much time did he exceed the specific time ?

 A) 2 days B) 3 days C) 4 days D) 5 days

Explanation:

work done=total number of person x number of days;
half of work done = 140 x 66;
For half of remaining work 25 extra men are added.
Therefore, total men for half work remaining = 140 + 25 = 165;
Let 2nd half work will be completed in K days;
140 x 66 = 165 x K
K = 122;
Hence, extra days => 122-120 = 2days.