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### #1. If A and B together can complete a piece of work in 15 days and B alone in 20 days, in how many days can A alone complete the work?

Answer: Option A
Solution:

1st method:
A and B complete a work in = 15 days
One day’s work of (A B) = 1/15

B complete the work in = 20 days;
One day’s work of B = 1/20

Then, A’s one day’s work

=1/151/20
=43/6
=1/60

Thus, A can complete the work in = 60 days.

2nd method:
(A B)’s one day’s % work = 100/15 = 6.66%
B’s one day’s % work = 100/20 = 5%
A’s one day’s % work = 6.66 – 5 = 1.66%
Thus, A need = 100/1.66 = 60 days to complete the work.

### #2. If A and B together can complete a work in 18 days, A and C together in 12 days, and B and C together in 9 days, then B alone can do the work in:

Answer: Option B
Solution:
One day’s work of (A B) = 118.......(1)
One day’s work of (A C) =112.......(2)
One day’s work of (B C)=19.......(3)
Adding(1),(2) and (3)
2×(A B C)
={(1/18) (1/12) (1/9)}=1/4
One day’s work of (A B C)=1/8
B=(1/8)(A C)
B=(1/8)(1/12)
One day’s work of
B=(32)/24
=1/24
B need 24 days

### #3. A and B together can complete a work in 3 days. They start together but after 2 days, B left the work. If the work is completed after two more days, B alone could do the work in

Answer: Option B
Solution:

1st Method:
(A B)’s one day’s work = 1/3 part
(A B) works 2 days together = 2/3 part
Remaining work = 12/3 =1/3 part

1/3 part of work is completed by A in two days

Hence, one day’s work of A = 1/6

Then, one day’s work of B =

1/31/6 1/6

So, B alone can complete the whole work in 6 days.

2nd Method:
(A B)’s one day’s % work = 100/3 = 33.3%
Work completed in 2 days = 66.6%
Remaining work = 33.4%
One day’s % work of A = 33.4/2 = 16.7%
One day’s work of B = 33.3 – 16.7 = 16.7%
B alone can complete the work in,

= 100/16.7 = 6 days.

### #4. A can complete a piece of work in 18 days, B in 20 days and C in 30 days, B and C together start the work and forced to leave after 2 days. The time taken by A alone to complete the remaining work is:

Answer: Option C
Solution:

1st Method:

(B C)s 2 days work
=2×(1/20 1/30)
=2×(3 2/60)
=1/6 part
Remaining work =11/6
=5/6 part
A’s one day’s work=1/18 part
Time taken to complete the work=(5/6)/(1/18) days
Hence,Time taken to complete the work
=(5/6)×18 = 15 days

2nd Method:
% of work B completes in one day = 100/20 = 5%;
% of work C completes in one day = 100/30 = 3.33%;
% of work (A B) completes together in one day = 5 3.33 = 8.66%;
% work (A B) completes together in 2 days = 8.66 × 2 = 17.32%;
Remaining work = 100 – 17.32 = 82.68%;
% of work A completes in 1 day = 100/18 = 5.55%
Time taken to complete the remaining work by A = 82.68/5.55 = 15 days

### #5. Working 5 hours a day, A can Complete a work in 8 days and working 6 hours a day, B can complete the same work in 10 days. Working 8 hours a day, they can jointly complete the work in:

Answer: Option A
Solution:

1st Method:
Working 5 hours a day, A can complete the work in 8 days i.e.
= 5 × 8 = 40 hours
Working 6 hours a day, B can complete the work in 10 days i.e.
= 6 × 10 = 60 hours
(A B)’s 1 hour’s work,

=1/40 1/60
=3 2/120
=5/120
=1/24

Hence, A and B can complete the work in 24 hours i.e. they require 3 days to complete the work.

2nd Method:
% 1 hour’s work of A = 100/40 = 2.5%
% 1 hour’s work of B = 100/60 = 1.66
(A B) one hour’s % work,

= (2.5 1.66) = 4.16%
Time to complete the work,
= 100/4.16 = 24 hours
Then,

24/8 = 3 days

They need 3 days, working 8 hours a day to complete the work.

### #6. Ganga and Saraswati, working separately can mow field in 8 and 12 hours respectively. If they work in stretches of one hour alternately. Ganga is beginning at 9 a.m., when will the moving be completed?

Answer: Option C
Solution:

1st Method:
Whenever, workers are working alternatively on one work, we take 2 as 1 unit
In this case, we take 2 hours as 1 unit.
Part of the field moved by Ganga and Saraswati in 2 hours (1 unit) = 1/8 1/12 = 5/24

Time taken to complete the work,= 1/5/24 =24/5 unit of time
Then actual time taken by them to complete the work,

2×24/5 = 9.6 hours
The work starts at 9 a.m. then it will complete at 6:36 pm

2nd Method:
% of the field moved by Ganga and Saraswati in 2 hours (1 unit),

(100/8)%  (100/12)%
= 12.5 8.33
= 20.83%; Time taken to move the whole field,
= 100%/20.83%

= 4.8 unit of time;
Hence, actual time = 2 × 4.8 = 9.6 hours.
The work starts at 9 a.m. then it will complete at 6:36 pm

### #7. If 10 men can do a piece of work in 12 days, the time taken by 12 men to do the same piece of work will be:

Answer: Option B
Solution:

Here, we use work equivalence method;
10*12 = 12*x;
Or, x = 10 days;

To understand the work equivalence method, we use a graphic as follows:

Men   Days
10 ↓    12
12     ↑ x (let)
Here, the two arrows, downward (↓) and upward (↑) show variation between men and days.
[If downward arrows show decrements then upward arrows show increments and vice-verse.]
Thus,

10/12 = x/12
or,
x=10×12/12
=10 days

### #8. To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?

Answer: Option A
Solution:
We have B=32×A
A=2/3×B
One day’s work, A B=1/18
2/3×B B=1/18
5/3×B=1/18
One day’s work of B=3/90

B alone can complete the work in

= 90/3
=30 days

### #9. If 10 men or 20 boys can make 260 mats in 20 days, then how many mats will be made by 8 men and 4 boys in 20 days?

Answer: Option A
Solution:

10 men = 20 boys
→1 men = 2 boys
8 men = 2 × 8 boys = 16 boys
Then,
(16 boys 4 boys) = 20 boys can make 260 mats in 20 days
Now,
It can be calculated by work equivalence method:
20 × 260 × 20 = x × 20 × 20
x = 260 mats

### #10. A complete 7/10 of a work in 15 days, then he completed the remaining work with the help of B in 4 days. In how many day A and B can complete entire work together?

Answer: Option C
Solution:
7/10 part of work has been completed by A in 15 days. Then,

Rest work = 1 –  7/10 = 3/10 part
Given, That

3/10 part of the work is completed by A and B together in 4 days. Means,

(A B) completed the  3/10 of work in 4 days
So, (A B)’s 1 day’s work =

3/10×4  = 3/40

Hence,
(A B) can complete the work in

40/3 days