15 men

can type

3240 pages

in

6 days

working

2 hours per

a day. how many men would be required to type

5400 pages

working

4 hours

per day for

3 days?

Sol:

P1 = 15

W1 = 3240

H = 2

D = 6

P2 = ? (x)

W2 = 5400

H = 2

D = 3

* Work is given .:. Then use formula 1

**Ex II :**

If 72 men can build a wall of

280 m length

, in

21 days

how many men could take

18 days

to build similar type of wall of length

100 m?

If 72 men can build a wall of

280 m length

, in

21 days

how many men could take

18 days

to build similar type of wall of length

100 m?

**Sol:**

**P1 = 72**

D1 = 21

W1 = 280

D1 = 21

W1 = 280

**P2 = ? (x)**

D2 = 18

W2 = 100

D2 = 18

W2 = 100

*** Work is given then use formula 1**

(iii)

39 persons

can repair a road in

12 days

working

5 hours

a day. in how many days will

30 persons

working

6 hours

a day complete the work.

Sol:

P1 = 39

D1 = 12

H1 = 5hours

P2 = 30

D2 = ? (x)

H2 = 6 hours

* work is not given, then use formula - 2

P1

H1

D1 =

P2

H2

D2

39 x 5 x 12 = 30 x

X

x 6

x = 13

(iv)

15 labours

complete a work in

10 days

working

6 hours

per day, if

18 labours

employed on that work and the work is to be completed in

5 days

then how many hours per day should the work be continued

Sol:

P1 = 15

;

D1 = 10

H1 = 6

P2 = 18

;

D2 = 5

H2 = ? (X)

* Working not given, then use formula 2

**.:. P1 H1 D1 = P2 H2 D2**

**15 x 6 x 10**

= 18 x X x 5

= 18 x X x 5

**.:. x = 10**

**Type II**

**Based on efficiency**

**1. A is two times efficient then B =>**

**A B**

**5 Days 10 days**

**x**

**2x**

x2

(ii) A is trice times efficient than B

=> A B

10 days 30 days

**x**

3x

(ii) A is four times efficient than B

=> A B

10 days 40 days

**x**

4 x X

4.

A is 50%

"more efficient" then

B

A

B

100%

150%

A

B

5.

A takes 50%

"more time"

than B

x

+

50% of x

For more complex problems

Ex:-

"A"

is twice as good

"B"

and

"B"

is twice as good as

"C"

if A and B can together finish a piece of work in

4 days

The

"C"

can do it by himself in:

Sol:

A B C

x days 2x 4x

* A + B completes a task in 4 days

.:. 1 day work => A + B

=

(ii)

A and B

together can do a work in

12 days.

B and C together do it in

15 days

. If A's efficiency is twice that of C,

Then The required for B alone to finish the work is.

let us take 1 day of work

B alone to finish the work alone is

.:. Substitute x value in Equation (i)

**.:. B takes 20 Days**

(iii) asha and Babu can do a job together in

7 days

Asha is 1 times as efficient as babu. Same job can be done by asha alone in?

let us take 1 day work

(iv) A can do a piece of work in

70 days

and B is

40% more efficient

than A. Then the number of days taken by B to do the same work is.

Sol :

A

B

70 days x days

140% 100 %

* B is more 40% Efficient Than

"A"

.:. B A

100% 140%

140% = 70 days

100% = x

.:. Remove (or) cancel percentages and cross multiply

140 x = 70 x 100

x = 50 days

(v) To complete a work.

A takes 50%

more time than B. if together they take

18 days

to complete work,

how much time shall B take to do it?

Sol:

A

B

x

+

50 of x

x

**Type- III : Fraction of Work:-**

Ex-(i) A can complete of a work in 4 days and B can complete of the work in 6 days.

in how many days can both A and B together complete the work?

Sol:

Ex (ii):

A can do of a piece of work in

5 days,

B can do of the same work in

9 days

and C can do of that work in 8 days. in how many day can all of them together do the work?

Sol:

(iii)

Sol:

(iii) A does work of a piece of work in

20 days

he calls B and they finish the remaining work in

3 days

how long B alone will take to do the whole work?

Sol:

(iv) A does

1/10 part of work

in

15 days

after that he completes the remaining work in

4 days

with the help of B

in how many days will A and B. Together do the same work?

Sol:

(v) A complete

2/3

of his work in

10 days.

Time he will take to complete

3/5

of the same work is .

**Sol:**

**Step 1:**

**One day work done**

**Step 2:**

**Find Ratio**

**Step 3:**

**Find Share**

1)

A can do work in

3 days.

B can do the same work in

2 days.

Both of them finish the work together and get

Rs.150

what is the share of A?

Sol:

2)

A and B under took to do a piece of work for

Rs. 4500

Alone could do it in

8 days

and B alone in

12 days

With the assistance of C they finished the work in

4 days

then C's share of money is:

Sol:

3. Three persons undertake to complete a piece of work for

1200 Rs.

the first person can complete the work in

8 days

second person in

12 days.

and third person in

16 days

They complete the work with the help of a fourth person in

3 days.

What does the fourth person get?

**Sol:**

4.

A, B, C

completed work costing

Rs.1800

A worked for

6 days

, B for

4 days

and C for

9 days,

If their daily wages are in the ratio of

5 : 6 : 4

, how much amount will be received by A?

Sol:

Daily wages

=>

5 : 6 : 4

6 x 4

4 x 6

9 x 4

A : B : C = 5 : 4 : 6

120

5.

a man and a boy received

Rs.800

as wages for

5 days

for the work they did together. The man's efficiency in the work was three times that of the boy.

what are the daily wages of the boy?

Sol:

**M + B = 5 days = 800**

the man efficiency

is trice than the Boy

In term of days

in term of work

x : 3x

5 : 15

3 : 1

M : B

x3

6.

If

5 Men

(or)

7 women

can Earn

Rs.5250

Per day. How would

7 men

and

13 women

Earn per day?

Sol:

5 men = 5250

1 men = 1050

7 men = 1050 x 7

= 7350

1 men =

7 women = 5250

1 women =

1 women = 750

13 women = 750 x 13

= 9750

17 , 100

7

.

2 men

and

1 women

together can complete a piece of work in

14 days,

while

4 women

and

2 men

together can do it in

8 days.

If a man gets

Rs.600

per day, how much should a woman get per day?

Sol:

SHORT CUT

8.

A, B, C

together Earn

Rs.150

per day while A and C together Earn Rs.94 and B & C together Earn Rs.76 The daily Earning of 'C' is ?

Sol:

1.

A and B

together can complete a work in

3 days

they started but after

2 days

B left the work. If the work is completed after

2 more

days.

B

alone could do the work in how many days?

sol:

Normal Method:

2.

Ajay can do a piece of work in

25 days

and sanjay can finish it in

20 days.

They work together for

5 days

and then ajay goes away. In how many days will sanjay finish the remaining work?

Sol:

Short cut :2

3.

A and B

can do a piece of work in

60 days

and

75 days

respectively. Both begin together but after a certain time

A

leaves off. In such case,

B

finishes the remaining work in

30 days.

After how many days did A leave?

short cut :1

Normal method

Short cut : 2

4.

A

can complete a piece of work in

40 days

. He starts working, but having some other engagement leaves after

5 days.

Thereafter,

B

completes this work in

21 days.

How many days would A and B take to complete this work working together?

Sol:

Normal method

Short cut I:

short cut: II

1.

Ajay and sunil together can complete a piece of work in

10 days.

sunil and sanjay in

15 days

and sanjay and Ajay in

20 days,

They worked together for

6 days,

and then ajay leaves. Sunil and sanjay worked together for

4 more days

and sunil leaves.

How long will sanjay take to complete the work?

Sol:

2.

A, B and C can do piece of work in

16, 32 and 48

days respectively. They all begin together. A work continuously till it is finished,

C leaves

the work

2 days

before its completion. and B leaves the work the work 1 day before its completion,

In what time is the work finished?

Sol:

3.

A and B

can finish a job in

10 days,

while

B and C

can do it in

18 days.

A

started the job and worked for

5 days

and left the job . Then

B

worked for

10 days

and remaining job is finished by

C

in

15 days.

In how many days

C

alone have finished whole job?

Sol:

x

.:.

.:.

**=**

4

2

1

15

**10 days**

8

=>

(A +B) x

39

120

3

10

4.

A can complete a piece of work in

40 days

.

He starts working, but having some other engagement leaves after 5 days. Thereafter

B

completes this work in

21 days

.

How many days would A and B take to complete this work working together?

sol:

Normal Method

Ex 1:

15 men

can type

3240 pages

in

6 days

working

2 hours per

a day. how many men would be required to type

5400 pages

working

4 hours

per day for

3 days?

Ex II :

If 72 men can build a wall of

280 m length

, in

21 days

how many men could take

18 days

to build similar type of wall of length

100 m?