**1.**A and B

together can do a piece of work in 30 days. A having worked for 16 days, B

finishes the remaining work alone in 44 days. In how many days shall B finish

the whole work alone?

(1) 40days (2) 30

days

days

(3)

60 days

50 days

60 days

**(4)**50 days

**2.**A and B can do a job together in 7

days. A is 1 3 /4 times as

efficient as B. The same job can be done by A alone in :

(1) 12 days (2) 11 days

(3) 15 days (4) 16 days

**3.**X can do a piece of work in 40 days.

He works at it for 8 days and then Y finished it in 16 days. How long will they

together take to complete the work?

(1) 13 1/3 days (2)15 days

(3)16 days (4) 17 days

**4.**A can finish a work in 24 days, B in 9

days and C in 12 days. B and C start the work but are forced to leave after 3

days. The remaining work was done by A in:

(1) 15 days (2) 10 days

(3) 12 days (4) 14 days

**5.**A and B can do a work in 8 days, B and

C can do the same work in 12 days. A, B and C together can finish it in 6 days.

A and C together will do it in :

(1) 4 days (2) 8

days

days

(3) 6days (4) 7

days

days

**6.**Twenty women can do a work in sixteen

days. Sixteen men can complete the same work in fifteen days. What is the ratio

between the capacity of a man and a woman?

(1) 4 : 3 (2) 3: 4

(3) 5 : 3 (4)

3: 5

3: 5

**7.**A works twice as fast as B. If B can

complete a work in 12 days independently, the number of days in which A and B

can together finish the work in :

(1) 4 days

8 days

**(2)**8 days

(3) 2 days (4) 5

days

days

**8.**A and B can complete a work in 15 days

and 10 days respectively. They started doing the work together but after 2 days

B had to leave and A alone completed the remaining work. The whole work was

completed in :

(1) 16 days (2) 14 days

(3) 18 days (4) 12 days

**9.**A takes twice as much time as B or

thrice as much time as C to finish a piece of work. Working together, they can

finish the work in 2 days. B can do the work alone in:

(1) 6 days (2) 12 days

(3) 8 days (4)7

days

days

**10.**Sakshi can do a piece of work in 20

days. Tanya is 25% more efficient than Sakshi. The number of days taken by

Tanya to do the same piece of work is

(1) 8 days (2) 15

days

days

(3) 16 days (4) 13

days

days

**ANSWERS**

**1.**(3)

**Explanation:**

Let

A’s 1 day’s work = x and B’s 1 day’s work = y.

Both A’s and B’s 1 day work=1/30

i.e (A’s 1 day + B’s 1 day)=1/30

i.e x + y = 1/30……..eq1

now,

A having worked for 16 days, B finishes the remaining work alone in 44 days

i.e work done by A in 16 days = 16x

Remaining work done B= 1 – 16x

but Remaining work is done by B in 44days i.e 44y

i.e. 44y=1-16x

i.e 16x+44y=1……..eq2

solving eq1 & eq2,

we get,x = 1/60 and y = 1/60

B’s 1 day’s work = 1/60.

Hence, B alone shall finish the whole work in

A’s 1 day’s work = x and B’s 1 day’s work = y.

Both A’s and B’s 1 day work=1/30

i.e (A’s 1 day + B’s 1 day)=1/30

i.e x + y = 1/30……..eq1

now,

A having worked for 16 days, B finishes the remaining work alone in 44 days

i.e work done by A in 16 days = 16x

Remaining work done B= 1 – 16x

but Remaining work is done by B in 44days i.e 44y

i.e. 44y=1-16x

i.e 16x+44y=1……..eq2

solving eq1 & eq2,

we get,x = 1/60 and y = 1/60

B’s 1 day’s work = 1/60.

Hence, B alone shall finish the whole work in

**60 days.****2.**(2)

Explanation:

(A’s

1 day’s work) : (B’s 1 day’s work) = 7 /4 : 1 = 7 : 4

1 day’s work) : (B’s 1 day’s work) = 7 /4 : 1 = 7 : 4

Let

A’s and B’s 1 days’ work be 7 x and 4 x

respectively

A’s and B’s 1 days’ work be 7 x and 4 x

respectively

then

, 7x + 4 x= 1/7 à 11 x = 1/7 à x = 1/77

, 7x + 4 x= 1/7 à 11 x = 1/7 à x = 1/77

A’s 1 days = 1 / 77 x 7 =

**1/ 11**
Hence, A alone shall finish the whole work in

**11 days.****3.**(1)

Explanation:

Work

done by X in 8 days = ( 1 / 40 x 8 ) = 1/5

done by X in 8 days = ( 1 / 40 x 8 ) = 1/5

Remaining

work ( 1 – 1/ 5 ) = 4/ 5

work ( 1 – 1/ 5 ) = 4/ 5

Now,

4/ 5 work is done by Y in 16 days

4/ 5 work is done by Y in 16 days

Whole

work will be done by Y in ( 16 x 5 / 4 ) = 20

days

work will be done by Y in ( 16 x 5 / 4 ) = 20

days

So, X’s 1 days work = 1/ 40 , Y’s 1 day’s work =

1 / 20

1 / 20

(

X+ Y )’s 1 days’ work = ( 1/ 40

+ 1/ 20 ) = 3 / 40

X+ Y )’s 1 days’ work = ( 1/ 40

+ 1/ 20 ) = 3 / 40

Hence

, X and Y will together complete the

work in ( 40 / 3) =

, X and Y will together complete the

work in ( 40 / 3) =

**13 1/ 3 days****4.**(2)

**Explanation**:

Total

Unit of work=LCM(Time taken by A,Time taken by B,Time taken by

c)=LCM(24,9,12)=72

A’s 1 day work=72/24=3unit

B’s 1 day work=72/9=8 unit

C’s 1 day work=72/12=6unit

work done by(B+C) in 1 day=(8+6)unit=14 unit

work done by(B+C) in 3 day=14×3=42 unit

Remaing work=(Total work – work done by B+C in 3 days)= (72-42)=30unit

Remaing work done by A in=Remaining work/A’s 1 day work= 30/3=

Unit of work=LCM(Time taken by A,Time taken by B,Time taken by

c)=LCM(24,9,12)=72

A’s 1 day work=72/24=3unit

B’s 1 day work=72/9=8 unit

C’s 1 day work=72/12=6unit

work done by(B+C) in 1 day=(8+6)unit=14 unit

work done by(B+C) in 3 day=14×3=42 unit

Remaing work=(Total work – work done by B+C in 3 days)= (72-42)=30unit

Remaing work done by A in=Remaining work/A’s 1 day work= 30/3=

**10 days****5.**(2)

Explanation:

(A+B+C)=1/6

A’s one day work work= (A+B+C)-(B+C)= 1/6-1/12 =1/12

C’s one day work work= (A+B+C)-(A+B)= 1/6-1/8= 1/24

(A+C)’s one day work= 1/12+1/24= 1/8

so the work will be completed in

A’s one day work work= (A+B+C)-(B+C)= 1/6-1/12 =1/12

C’s one day work work= (A+B+C)-(A+B)= 1/6-1/8= 1/24

(A+C)’s one day work= 1/12+1/24= 1/8

so the work will be completed in

**8 days****6.**(1)

**Explanation**:

(20

x 16) women can complete the work in 1 day

x 16) women can complete the work in 1 day

1

woman’s 1 day’s work = 1/ 320

woman’s 1 day’s work = 1/ 320

16

x 15) men can complete the work in 1 day

x 15) men can complete the work in 1 day

1

man’s 1 day’s work = 1/240

man’s 1 day’s work = 1/240

required

ratio =1/240:1/320.

Now (1/240)/(1/320).

By solving:

(1/240)*(320/1)

=320/240

=4/3 i.e.

ratio =1/240:1/320.

Now (1/240)/(1/320).

By solving:

(1/240)*(320/1)

=320/240

=4/3 i.e.

**4:3.****7.**(1)

**Explanation**:

B’S

one day work=1/12

A’S one day work=2(1/12)=1/6

(A+B) one day work=(1/12)+(1/6)=1/4

hence A and B together complete the work in

one day work=1/12

A’S one day work=2(1/12)=1/6

(A+B) one day work=(1/12)+(1/6)=1/4

hence A and B together complete the work in

**4 days**

**8.**(4)

**Explanation**:

A’s

1 day work=1/15

B’s 1 day work=1/10

now,B left after 2 days then 1/10*2=1/5

remaining work is (1-1/5)=4/5

4/5 work is left by B then A has to do remaining work (1/15*5/4)=1/12 this is

A’s 1 day work after B left work

now A completes work in

1 day work=1/15

B’s 1 day work=1/10

now,B left after 2 days then 1/10*2=1/5

remaining work is (1-1/5)=4/5

4/5 work is left by B then A has to do remaining work (1/15*5/4)=1/12 this is

A’s 1 day work after B left work

now A completes work in

**12 days…**

**9.**(1)

**Explanation**:

A

takes twice much time them B i.e. 2A=B…(i)

A takes thrice much time thn C i.e. 3A=C…(ii)

It is given dat workin together they can finish in 2 days

so A+B+C=1/2

Now put B=2A AND C=3A in this equ…

A+B+C=1/2

A+2A+3A=1/2

6A=1/2

A=1/2*6=1/12

Now put the value of A in equ.(i)

.i.e B=2A

=2*1/12

=1/6

Therefore B takes

takes twice much time them B i.e. 2A=B…(i)

A takes thrice much time thn C i.e. 3A=C…(ii)

It is given dat workin together they can finish in 2 days

so A+B+C=1/2

Now put B=2A AND C=3A in this equ…

A+B+C=1/2

A+2A+3A=1/2

6A=1/2

A=1/2*6=1/12

Now put the value of A in equ.(i)

.i.e B=2A

=2*1/12

=1/6

Therefore B takes

**6 days**to complete the work.**10.**(3)

**Explanation**:

Tanya

is 25% more efficient than Sakshi.

Tanya is 125.

Sakshi is 100.

Ratio of efficiency is 5:4.

So, ratio of time will be 4:5.

Given, Sakshi can do work in 20 days means 5*4=

In the same way for Tanya 4*4=

is 25% more efficient than Sakshi.

Tanya is 125.

Sakshi is 100.

Ratio of efficiency is 5:4.

So, ratio of time will be 4:5.

Given, Sakshi can do work in 20 days means 5*4=

**20.**In the same way for Tanya 4*4=

**16.**