**Unitary Method Time and Work :**

In this section, we are going to see, how to solve time and fork problems using unitary method.

**Unitary Method Definition and Example :**

**Definition :**

Unitary-method is all about finding value to a single unit.

**Example :**

If 8 men can complete a work in 6 days,

1 men can complete in = 8 x 6 = 48 days.

**Tricks to solve time and work problems using unitary method : **

(i) If A can complete a work in "m" days, then part of the work completed by A in 1 day is 1/m.

(i) If A can complete 1/m part of the work in 1 day, then A will complete the work in "m" days.

**Problem 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?

**Solution : **

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

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

Let us look at the next problem on "Unitary method time and work"

**Problem 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 ?

**Solution : **

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

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

Let us look at the next problem on "Unitary method time and work"

**Problem 3 :**

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

**Solution : **

**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

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

Let us look at the next problem on "Unitary method time and work"

**Problem 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 ?

**Solution : **

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

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

Let us look at the next problem on "Unitary method time and work"

**Problem 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 ?

**Solution : **

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

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

Let us look at the next problem on "Unitary method time and work"

**Problem 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 ?

**Solution : **

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

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

Let us look at the next problem on "Unitary method time and work"

**Problem 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 ?

**Solution : **

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

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

Let us look at the next problem on "Unitary method time and work"

**Problem 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 ?

**Solution : **

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

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

After having gone through the stuff given above, we hope that the students would have understood "Unitary method for time and work".

Apart from the stuff given above, if you want to know more about "Unitary method for time and work", please click here

Apart from the stuff given on "Unitary method for time and work", if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

HTML Comment Box is loading comments...