Worksheet given in this section will be much useful for the students who would like to practice word problems on unitary method.

Before look at the worksheet, if you would like to know the basic stuff about unitary method,

**Question 1 :**

A can do a piece of work in 15 days while B can do it in 10 days. How long will they take together to do it ?

**Question 2 :**

A, B and C can do a piece of work in 12 days, 15 days and 10 days respectively. In what time will they all together finish it ?

**Question 3 :**

5 workers can complete a work in 20 days. In how many days can 10 workers complete the same work ?

**Question 4 :**

A and B together can do a piece of work in 35 days, while A alone can do it in 60 days. How long would B alone take to do it ?

**Question 5 :**

A can do a piece of work in 20 days while B can do it in 15 days. With the help of C, they finish the work in 5 days. In what time would C alone do it ?

**Question 6 :**

A can do a piece of work in 12 days and B alone can do it in 16 days. They worked together on it for 3 days and then A left. How long would B take to finish the remaining work ?

**Question 7 :**

A can do 1/4 part of a work in 5 days, while B can do 1/5 part of the work in 6 days. In how many days can both do it together ?

**Question 8 : **

A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely ?

**Question 1 :**

A can do a piece of work in 15 days while B can do it in 10 days. How long will they take together to do it?

**Answer : **

A’s 1 day work = 1/15

B’s 1 day work = 1/10

(A + B)’s 1 day work = 1/15 + 1/10

L.C.M of (15, 10) = 30.

Then, we have

(A + B)’s 1 day work = 2/30 + 3/30

(A + B)’s 1 day work = 5/30

(A + B)’s 1 day work = 1/6

So, A and B can together finish the work in 6 Days.

**Question 2 :**

A, B and C can do a piece of work in 12 days, 15 days and 10 days respectively. In what time will they all together finish it ?

**Answer :**

A’s 1 day work = 1/12

B’s 1 day work = 1/15

C’s 1 day work = 1/10

(A + B + C)’s 1 day work = 1/12 + 1/15 + 1/10

L.C.M of (12, 15, 10) = 60.

Then, we have

(A + B + C)’s 1 day work = 5/60 + 4/60 + 6/60

(A + B + C)’s 1 day work = 15/60

(A + B + C)’s 1 day work = 1/4

So, A, B and C can together finish the work in 4 days.

**Question 3 :**

5 workers can complete a work in 20 days. In how many days can 10 workers complete the same work ?

**Answer :**

**Given : **5 workers can complete the work in 20 days

Number of days taken by one worker to complete the same work is

= 5 ⋅ 20 days

= 100 days

Number of days taken by 10 workers to complete the same work is

= 100 / 10 days

= 10 days

So, 10 workers can complete the work in 10 days.

**Question 4 :**

A and B together can do a piece of work in 35 days, while A alone can do it in 60 days. How long would B alone take to do it ?

**Answer :**

Let "x" be the no. of days taken by B to complete the work.

A’s 1 day work = 1/60

B’s 1 day work = 1/x

(A + B)’s 1 day work = 1/60 + 1/x

L.C.M of (60, x) = 60x.

Then, we have

(A + B)’s 1 day work = (x/60x) + (60/60x)

(A + B)’s 1 day work = (x + 60)/60x ------(1)

**Given :** A and B together can do the work in 35 days.

So, we have

(A + B)’s 1 day work = 1/35 ------(2)

From (1) and (2), we get

(x + 60)/60x = 1/35

35(x + 60) = 1 ⋅ 60x

35x + 2100 = 60x

2100 = 25x

84 = x

So, B alone can complete the work in 84 Days.

**Question 5 :**

A can do a piece of work in 20 days while B can do it in 15 days. With the help of C, they finish the work in 5 days. In what time would C alone do it ?

**Answer :**

Let "x" be the no. of days taken by C to complete the work.

A’s 1 day work = 1/20

B’s 1 day work = 1/15

C’s 1 day work = 1/x

(A + B + C)’s 1 day work = 1/20 + 1/15 + 1/x

L.C.M of (20, 15, x) = 60x.

Then, we have

(A + B + C)’s 1 day work = (3x/60x) + (4x/60x) + (60/60x)

(A + B + C)’s 1 day work = (3x + 4x + 60)/60x

(A + B + C)’s 1 day work = (7x + 60)/60x ------(1)

**Given :** A, B and C together can do the work in 5 days.

So, we have

(A + B + C)’s 1 day work = 1/5 ------(2)

From (1) and (2), we get

(7x + 60)/60x = 1/5

5(7x + 60) = 1 ⋅ 60x

35x + 300 = 60x

300 = 25x

12 = x

So, C alone can complete the work in 12 Days.

**Question 6 :**

A can do a piece of work in 12 days and B alone can do it in 16 days. They worked together on it for 3 days and then A left. How long would B take to finish the remaining work ?

**Answer :**

A’s 1 day work = 1/12

B’s 1 day work = 1/16

(A + B)’s 1 day work = 1/12 + 1/16

L.C.M of (12, 16) = 48.

Then, we have

(A + B)’s 1 day work = 4/48 + 3/48

(A + B)’s 1 day work = 7/48

Then, the amount of work completed by A and B together in 3 days is

= 3 ⋅ 7/48

= 7/16

Amount of work left for B to complete is

= 9/16

Number of days that B will take to finish the work is

= Amount of work / part of the work done in 1 day

= (9/16) / (1/16)

= (9/16) ⋅ (16/1)

= 9

So, no. of days taken by B to finish the remaining work is 9 days.

**Question 7 :**

A can do 1/4 part of a work in 5 days, while B can do 1/5 part of the work in 6 days. In how many days can both do it together ?

**Answer :**

A’s 1 day work = (1/4) / 5 = 1/20

B’s 1 day work = (1/5) / 6 = 1/30

(A + B)’s 1 day work = 1/20 + 1/30

L.C.M of (20, 30) = 60.

Then, we have

(A + B)’s 1 day work = 3/60 + 2/60

(A + B)’s 1 day work = 5/60

(A + B)’s 1 day work = 1/60

So, A, and B can together finish the work in 60 days.

**Question 8 : **

A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely ?

**Answer :**

A’s 1 minute work = 1/10

B’s 1 minute work = 1/6

(A + B)’s 1 minute work = 1/10 - 1/6

L.C.M of (10, 6) = 30.

Then, we have

(A + B)’s 1 minute work = 3/30 - 5/30

(A + B)’s 1 minute work = - 1/15

(A + B)’s 1 minute work = - 1/15

(Here, negative sign indicates that when both the pipers are opened together, 1/15 part of the tank will be emptied in 1 minute)

**Given :** 2/5 part of the tank is full

When both the pipes are opened, time taken to empty 2/5 part of the tank is

= Amount of water in tank / water emptied in 1 minute

= (2/5) / (1/15)

= (2/5) ⋅ (15/1)

= 6 minutes

So, when the tank is two-fifth full, if both the pipes are open, it will take 6 minutes to empty.

Apart from the problems on unitary method given above, if you need more problems on unitary method, please click the following links.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**

HTML Comment Box is loading comments...