In this section, the following topics are discussed with examples

**Formulae****Chain Rule****Examples**

### Formulae

If A can do a piece of work in n days.Then,A’s 1 day work

**A’s 1 day work=1/n**

In time and work Efficiency of a man is inversely proportional to time taken by the man to complete the work.

**Efficiency 𝛂 1/Time**

### Chain rule

In time and work, the chain rule is used when two or more components are given and one is missing to find the other.

**(M _{1} * D_{1} * T_{1})/W_{1} = (M_{2} * D_{2} * T_{2})/W_{2}**

## The only place where you will find success before work is in the dictionary.

May V Smith

#### Example 1:

A can do a piece of work in 30 days and B can do the same in 20 days. How many days it will take if they do the work together?

**Given:**

A’s total work done= 30 days

B’s total work done =20 days

To find

A+B how many days=?

**Sol**

A’s 1 day work=1/30

B’s 1 day work=1/20

(1/A+B)=1/30+1/20

=5/60

=1/12

Therefore,

A+B=12

So, A and B can complete the work in 12 days.

#### Example 2:

A can do a particular work in 6 days. B can do the same work in 8 days. A and B signed to do it for Rs. 4320. They completed the work in 3 days with the help of C. How much is to be paid to C?

**Given**

A’s work done= 6 days

B’s work done=8 days

A+B+C’s work=3 days

A and B get amount=4320

To find

How much salary C will get?

**Sol**

A’s 1 day work=1/6

B’s 1 day work=1/8

A + B + C’s 1 day work=1/3

A + B can complete = 1/6 + 1/8 =7/24

C’s 1 day work=1/3 – 7/24 =1/24

A’s 1 day work: B’s 1 day work: C’s 1 day work

=1/6:1/8:1/24 =4:3:1

Total work done in 1 day = 4 + 3 + 1 =8

Amount paid for c = 4320/8 = 540

#### Example 3:

9 men and 12 women finish a job in 12 days, 12 men and 12 women finish it in 10 days. 10 men and 10 women shall finish it in how many days?

**Given**

Men an M and Women as W

9M + 12W = 12—–(1)

12M+12W=10—–(2)

To find

10M+10w=? —–(3)

**Sol**

(1)*12 =>108M+144W

(2)*10 =>120M+120W

(1)=(2)=>12M=24W

=>M=2W —-(4)

Sub (4) in (1)

9M+6M=12

15M=12 —–(5)

Sub (4) in (3)

10M+5M=x

15M=X—-(6)

From (5) and (6)

10M+10W=12 days

#### Example 4:

A tank can be filled by a tap in 20 minutes and by another tap in 60 minutes. Both the taps are kept open for 10 minutes and then the first tap is shut off. After this, the tank will be completely filled in what time (min)?

a)10 b)20 c)15 d)25

**Soln: **b)20 min

Work done in 10 minutes =10 * [(1/20) + (1/60)] = ⅔

Remaining work=1 – ⅔ = ⅓

1/60 : ⅓ = 1:x

x=20