Q 1-If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be :

A - 4 days

B - 5 days

C - 6 days

D - 7 days

```Answer - A

Explanation

"Let 1 man's 1 day's work  = x
and 1 boy's 1 day's work = y.
Then ,
6x+8y=1/1
and 26x+48y=1 / 2
Solving these two equations,
we get : x=1 / 100 and y=1 / 200
(15 men + 20 boy's  1 day's work = (15 / 100 + 20 / 200) = 1 / 4
∴15 men and 20 boys can do the work in 4 days.
"
```

Q 2-4 men and 6 women can complete a work in 8 days , while 3 men and 7 women can complete if in 10 days. In how many days will 10 women complete it ?

A - 35

B - 40

C - 45

D - 50

```Answer - B

Explanation

"Let 1 man's 1 day's work = x
and 1 woman's 1 day's work = y.
Then,
4x+6y=1 / 8
And 3x+7y=1 / 10
Solving these wo equations,
we get  : x= 11 / 400, y=1 / 400
∴1 woman's 1 day's work =  1 / 400
⇒ 10 women's 1 day's  work = ([1 / 400]×10)= 1 / 40
Hence ,
10 women will  complete the work in 40 days.
"
```

Q 3-One man , 3 women and 4 boys can do a piece of work in 96 hours, 2 men and 8 boys can do it in 80 hours, 2 men and 3 women can do it in 120 hours. 5 men and 12 boys can do it in :

A - 39(1/11) hours

B - 42(7 / 11) hours

C - 43(7/11) hours

D - 44 hours.

```Answer - C

Explanation

"Let 1 man's 1 hours work = x,
1 woman's 1 hours work = y
and 1 boy's 1 hours work = z.
Then
x+3y+4z=1 / 96....................(I)
2x+8z=1 / 80......................(II)
2x+3y=1 / 120........................(III)
Adding (II) and (III) and subtracting (I) from it ,
we get  : 3x+4z=1 / 96........................(IV)
From (II) and (IV), we get x= 1 / 480.
Substituting ,
we get : y=1 / 720,z=1 / 960.
(5 men + 12 boy)'s 1 hour's work
=([5 / 480] +[12 / 960]) = (1 / 96+1 / 80)= 11 / 480.
∴5 men and 12 boys can do the work in 480 / 11 i.e. ,

43(7 / 11) hours
"
```

Q 4-If 12 men and 16 boys can do a piece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is :

A - 2 : 1

B - 3 : 1

C - 3 : 2

D - 5 : 4

```Answer - A

Explanation

"Let 1 man's 1 day's work = x
and 1 boy's 1 day's work = y.
Then,
12x+16y=1 / 5 and 13x+24y=1 / 4
Solving  these two equations ,
we get : x=1 / 100 and y=1 / 200
∴Required ratio = x : y=1 / 100 : 1 / 200

=  2 : 1
"
```

Q 5-5men and 2 boys working together can do four times as much work as a man and a boy. working capacities of a woman and a boy are in the ratio :

A - 1 : 2

B - 2 : 1

C - 1 : 3

D - 3 : 1

```Answer - B

Explanation

"Let 1 man's 1 day's work = x
and  1 boy's 1 day's work = y.
Then ,
5x+2y=4(x+y)  ⇒  x=2y    ⇒ x / y= 2 / 1

= 2 : 1
"
```

Q 6-24 men can complete a work in 16 days . 32 women can completes the same work in 24 days. 16 men and 16 women started working and worked for 12 days. How many more men are to be added to complete the remaining work in 2 days.

A - 16

B - 24

C - 36

D - 48

```Answer - B

Explanation

"1 man's 1 day's work = 1 / 384
1 woman's 1 day's work = 1 / 768
work done in 12 days = 12([16 / 384] +[16 / 768] )
=(12×[3 / 48] ) = 3 / 4
Remaining work = (1−[ 3 / 4] ) = 1 / 4
(16 men  + 16 women)'s  2 day's work
= 2([16 / 384] +[16 / 768] )=(2×[1 / 16] ) = 1 / 8
Remaining work = ([1 / 4] – [1 / 8] ) =1 / 8
1 / 384 work is done in 1 day by 1 man.
∴18 work will be done in 2 day by
(384×[1 / 8] ×[1 / 2] )

= 24 men.
"
```

Q 7-Sixteen men can complete a work in twelve days. Twenty-four children can complete the same work in eighteen days. Twelve men and eight children started working and after eight days three more children joined them. How many days will they now takes to complete the remaining work ?

A - 2 days

B - 4 days

C - 6 days

D - 8 days

```Answer - B

Explanation

"1 man's 1 day's work  = 1 / 192;
1 child's 1 day's work = 1 / 432
Work done in 8 days
= 8( [12 / 192] + [8 / 432] )
=8( [1 / 16] + [1 / 54] )=35 / 54
Remaining work = (1− [35 / 54] )=19 / 54
(12 men + 11 children)'s 1 day's work
= ( [12 / 192] + [11 / 432] )= 19 /216
Now,
19 / 216 work is done by  them in 1 day.
∴19 / 54 work will be done by  them in ( [216 / 19]× [19 / 54] )

=  4 days.
"
```

Q 8-10 women can complete a work in 7 days and 10 children take 14 days to complete he work . how many days will 5 women and 10 children take to complete the work ?

A - 3

B - 5

C - 7

D - Cannot be determined

```Answer - C

Explanation

"1 woman's 1 day's work = 1 / 70;
1 child's 1 day's work = 1 / 140
(5 women + 10 children)'s 1 day's work
= ( [5 / 70] + [10 / 140] )=( [1 / 14] + [1 / 14] )=1 / 7

∴5 women and 10 children will complete the work in 7 days.
"
```

Q 9-Twelve children take sixteen days to complete a work which can be completed by eight adults in twelve days . Sixteen adults started working and after three days ten adults left and four children joined them. How many days will they to complete he remaining work

A - 3

B - 4

C - 6

D - 8

```Answer - C

Explanation

"1 child's 1 day's work =  1 / 192
1 adult's 1 day's work = 196196
Work done in 3 days  = ( [1 / 96]×16×3) = 1 / 2
Remaining work = (1− [1 / 2] ) = 1 / 2.
(6 adults + 4 children)'s 1 day work
= ( [6 / 96 ]+ [4 / 192] )=1 / 12
1 / 12work is done by  them  in  1 day.
1 / 2work is done by them (12× [ 1 / 2] )

= 6 days.
"
```

Q 10-12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days. 6 men start working on the job and after working for 2 days. all of them stopped working . How many women should be put on he job to complete the remaining work . If it is to be completed in 3 days ?

A - 5

B - 18

C - 22

```Answer - A

Explanation

"1 man's 1 day's work = 1 / 48.
1 woman's 1 day's work = 1 / 60
6 men's 2 days' work = ( [6 / 48]×2) =1 / 4
Remaining work = (1−[1 / 4] ) = 3 / 4
Now, 1 / 60 work is done in 1 days by 1 woman.
So, 3 / 4 work will be done in 3 days by (60×[3 / 4]×[ 1 / 3] )
= 15 women.
"
```

Q 11-10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work ?

A - 125

B - 145

C - 150

D - None of these

```Answer - D

Explanation

"1 man's 1 day's work = 1 / 100
(10 men + 15 women)'s 1 day's work = 1 / 6
15 women's 1 day's work = ( [1 / 6] − [ 10 / 100] )
=( [1 / 6] − [ 1 / 10 ] )=1 / 15
woman's 1 day's work = 1 / 225

∴1 woman alone an complete the work in 225 days
"
```

Q 12-A man , a women and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1 / 4 of a day ?

A - 1

B - 4

C - 19

D - 41

```Answer - D

Explanation

"(1 man + 1 woman)'s 1 day's work
= ( [1 / 3] + [1 / 4]) = 7 / 12
Work done by  1 man and 1 woman  in  1 / 4 day
= ( [7 / 12] × [1 / 4] ) =7 / 48
Remaining work = (1− [7 / 48] ) = 41 / 48.
Work done by 1 boy in 1 / 4day
= ( [1 / 12] ×[1 / 4] ) =1 / 48.
∴Number of boys required  = ( [41 / 48] ×48)

=  41.
"
```

Q 13-Three men, four women and six children can complete a work in seven days. A woman does double the work a man does and a child does half the work a man does , How many women alone can complete this work in 7 days ?

A - 7

B - 8

C - 12

D - Cannot be determined

```Answer - A

Explanation

"Let 1 woman's  1 day's  work = x
Then ,
1 man's 1 day's  work = x / 2
and 1 child's  1 day's work =  x / 4
So,
( [3x / 2] + 4x + [6x4] ) = 1 / 7
⇒ 28x / 4 = 1 / 7
⇒  x =( [1 / 7]×[4 / 28] ) = 1 / 49.
∴1 woman alone can complete the work in  49 days.
So,
to complete the work in 7 days, number of women  required = 4 / 97

= 7
"
```

Q 14-12 men complete a work in 9 days. After they have worked for 6 days, 6 more men joint them . How many days will hey take to complete the remaining work ?

A - 2

B - 3

C - 4

D - 5

```Answer - A

Explanation

"1 man's 1 day's work = 1 / 108
12 men's 6 day's work = ([1 / 9]×6) = 2 / 3.
Remaining work = (1−[2 / 3] ) = 1 / 3
18 men's 1 day's work = ( [1 / 108] ×18) = 1 / 6
1 / 6 work is done by them in 1 day.
∴1 / 3 work is done by  them in (6× [1 / 3] )

=  2 days.
"
```

Q 15-Seven men can complete a work in 12 days. They started the work and after 5 days. two men left , In how many days will the work be completed by the remaining men ?

A - 6

B - 7

C - 8

D - None of these

```Answer - D

Explanation

"(7 x 12) men can complete the work in 1 day.
∴1 men's 1 day's work = 1 / 84
7 men's 5 day's work = ( [1 / 12]×5) = 5 / 12
Remaining work = (1− [5 / 12] ) =7 / 12
5 men's 1 day's work = ( [1 / 84]×5) =5 / 84.
5 / 84 work is done by them in 1 day
7 / 12 work is done by them in ( [84 / 5]×[7 / 12]) =49 / 5

= 9( 4/ 5)days.
"
```