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Time and Work
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 1

Explanation:

Solution:
1st method:
A and B complete a work in = 15 days
One day's work of (A + B) =
115

B complete the work in = 20 days;
One day's work of B =
120

Then, A's one day's work
=115120=436=160

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

2nd method:
(A + B)'s one day's % work =
10015
= 6.66%
B's one day's % work =
10020
= 5%
A's one day's % work = 6.66 - 5 = 1.66%
Thus, A need =
1001.66
= 60 days to complete the work.

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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 1

Explanation:

Solution:
Oneday'sworkof(A+B)=118.......(1)Oneday'sworkof(A+C)=112.......(2)Oneday'sworkof(B+C)=19.......(3)Adding(1),(2)and(3)2×(A+B+C)={(118)+(112)+(19)}=14One day's work of(A+B+C)=18B=(18)(A+C)B=(18)(112)One day's work ofB=(32)24=124Bneed24days

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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 1

Explanation:

Solution:
1st Method:

(A+B)'s one day's work =
13
part
(A+B) works 2 days together =
23
part
Remaining work =
123
  =
13
part
13
part of work is completed by A in two days
Hence, one day's work of A =
16

Then, one day's work of B =
1316
  =
16

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

2nd Method:
(A+B)'s one day's % work =
1003
= 33.3%
Work completed in 2 days = 66.6%
Remaining work = 33.4%
One day's % work of A =
33.42
= 16.7%
One day's work of B = 33.3 - 16.7 = 16.7%
B alone can complete the work in,
=
10016.7
= 6 days.

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4.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 1

Explanation:

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,
=140+160=3+2120=5120=124

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 =
10040
= 2.5%
% 1 hour's work of B =
10060
= 1.66
(A + B) one hour's % work,
= (2.5 + 1.66) = 4.16%
Time to complete the work,
=
1004.16
= 24 hours
Then,
248
= 3 days
They need 3 days, working 8 hours a day to complete the work.

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5.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 1

Explanation:

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) =
18
+
112
=
524

Time taken to complete the work,
=
1524
=
245
unit of time
Then actual time taken by them to complete the work,
=
2×245
  = 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),
=
(1008)%
  +
(10012)%

= 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.

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6.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 1

Explanation:

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,
1012=x12or, x=10×1212=10days

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7.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 1

Explanation:

Solution:
We haveB=32×AA=23×BOne day's work,A+B=11823×B+B=11853×B=118Oneday'sworkofB=390

B alone can complete the work in
=903=30days

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8.A complete
710
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 1

Explanation:

Solution:
710
part of work has been completed by A in 15 days. Then,
Rest work = 1 -
710
=
310
part
Given, That
310
part of the work is completed by A and B together in 4 days. Means,
(A + B) completed the
310
of work in 4 days
So, (A + B)'s 1 day's work =
310×4
  =
340

Hence,
(A + B) can complete the work in
403
=
1313
days

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9.A can complete a piece of work in 36 days, B in 54 days and C in 72 days. All the three began the work the work together but A left 8 days before the completion of the work and B 12 days before the completion of work. Only C worked up to the end. In how many days was the work completed?

Answer:Option 1

Explanation:

Solution:
Let the work be completed in x days. C work for x days then A works for (x - 8) days and B works for (x - 12) days.
According to the question,
[(x8)36+(x12)54+x72]=1[(6x48+4x48+3x)216]=113x96=21613x=216+96=312x=31212=24days

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10.While working 7 hour a day, A alone can complete a piece of work in 6 days and B alone in 8 days. In what time would they complete it together, 8 hour a day?

Answer:Option 1

Explanation:

Solution:
A can complete the work in 7 × 6 = 42 hours
1 hour's work of A =
142

B can complete the work in 7 × 8 = 56 hours
1 hour's work of B =
156

(A + B)'s 1 hour's work
=142+156=4+3168=7168

∴ Time taken by (A + B) working 8 hours daily
1687×8=3days

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