Time and Work
Aptitude

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Q.

12 men cam complete a piece of work in 36 days, 18 women can complete the same piece of work in 60 days. 8 men and 20 women work together for 20 days. If only women were to complete the remaining piece of work in 4 day, how many women would be required?

 A.

70

 B.

28

 C.

66

 D.

40

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Solution:
Option(A) is correct

12 men in 36 days can do a work.

1 man in a day can do \(\dfrac{1}{12\times 36}\)work.

8 men in 20 days can do \(\dfrac{8\times 20}{12\times 36}=\dfrac{10}{27}\) work.

Similarly, we find that 20 women in 20 days can do \(\dfrac{10}{27}\) work.

Remaining work = \(\dfrac{7}{27}\)

Now, because in 60 days a work is done by 20 women.

In 1 day a work done by $20\times 60$ women.

In 4 days \(\dfrac{7}{27}\) work is done by 

= \(\dfrac{20\times 60\times 7}{27\times 4}\)  = 70 women.


(2) Comment(s)


Harshit Varshney
 ()

12 men can complete a piece of work in 36 days

=> 1 man can complete the work in 36 × 12 days (∵ less man, more days. inversely proportional)

=> Work done by 1 man in 1 day =

1

36

×

12

136×12

18 women can complete the same piece of work in 60 days

=> 1 woman can complete the work in 60 × 18 days

=> Work done by 1 woman in 1 day =

1

60

×

18

160×18

Work done by 8 men and 20 women in 1 day =

8

36

×

12

+

20

60

×

18

=

1

54

+

1

54

=

1

27

836×12+2060×18=154+154=127

Work done by 8 men and 20 women in 20 days =

20

27

2027

Remaining work =

1

20

27

1−2027 =

7

27

727

Let n women complete this work in 4 days. Then

1

60

×

18

×

n

×

4

=

7

27

n

15

×

18

=

7

27

n

=

15

×

18

×

7

27

=

15

×

2

×

7

3

=

5

×

2

×

7

=

70

160×18×n×4=727n15×18=727n=15×18×727=15×2×73=5×2×7=70

Required number of women to complete the remaining work = 70



HEMANTH
 ()

60 days work done by 18 women .....but u have taken 20 instead of 18....