## Work and Wages

When a person receives some money for a certain work, the received money is called wages of the person for that particular work.

Total wages = Wages of 1 day work × Total number of days

**Example**: If Rohan's monthly wages ₹ 5400 and he work for all 30 days, then what will be his daily wages? **Solution:** Let the daily wages be x.

Total wages = Daily wages × Total number of days

⇒ 5400 = x × 30

⇒ x = | = 180 | |||

30 |

### Important Points

- Wages is directly proportional to the work done.
- More money will be received for more work and less money will be received for less work.
- Wages is indirectly proportional to the time taken by the individual.

**Example:** If A can do a piece of work in 15 days and B can do the same piece of work in 20 days. Then, ratio of A and B's daily wage will be

20 : 15 = 4 : 3.

### Some Important Rule

**Rule** **1**: If P can do a piece of work in x days and Q can do the same work in y days, the ratio of their wages will be y : x. Then the wages earned by P and Q will be

P's wages = | × y | |

(x + y) |

Q's wages = | × x | |

(x + y) |

**A can do a piece of work in 5 days, while B can do the same work in 7 days. If the total amount to be given for this work is ₹ 7200, then what will be the share of A, if both work together?**

Example:

Example:

**Solution**:- Time taken by A = 5 days

A's one day work = | ||||

5 |

B's one day work = | ||||

7 |

Ratio of their incomes = | : | = 7 : 5 | |||||

5 | 7 |

∴ A's share = | × 5 = | × 5 | |||||

( 7 + 5 ) | 12 |

**Example:**A can do a piece of work in 5 days while B can do the same work in 6 days. If they work together for a total wages of ₹ 5500, how much does A get?

**Solution**: Time taken by A = 5 days

A's one day work = | ||||

5 |

A's one day work = | ||||

6 |

Ratio of their incomes = | : | = 6 : 5 | |||||

5 | 6 |

∴ A's share = | × 5 = | × 6 | |||||

( 6 + 5 ) | 11 |

**Rule** **2:** If P, Q and R can do a piece of work in x, y and z days respectively, the ratio of their wages will be yz : xz : xy. Then, wages earned by P, Q and R respectively will be

P's wages = | × yz | |

( xy + yz + zx ) |

Q's wages = | × xz | |

( xy + yz + zx ) |

R's wages = | × xy | |

( xy + yz + zx ) |

**Example:**A, B and C take ₹ 470 for doing a piece of work together. If working alone, each takes 3 days, 4 days and 5 days respectively, then find the share of each.

**Solution**:- Total amount earned = ₹ 470

Ratio of their incomes = | : | : | ||||||||

3 | 4 | 5 |

= | × 60 : | × 60 : | × 60 = 20 : 15 : 12 | |||||||

3 | 4 | 5 |

∴ A's share = | × 20 = ₹ 200 | |||

47 |

B's share = | × 15 = ₹ 150 | |||

47 |

C's share = | × 12 = ₹ 120 | |||

47 |

**Rule 3:** P can do a piece of work in x days. With the help of Q, P can do the same work in y days. If they get ₹ a for that work, then

Share of P = ₹ | ||

x |

Share of Q = ₹ | ||

x |

**Example:**A Can do a work in 30 days. A and B together do the same work in 25 days. If they got ₹ 3000 for that work, then find the share of A and B.

**Solution**:

A's one day work = | ||

30 |

( A + B )'s one day work = | ||

25 |

B's one day work = | - | = | ||||||

25 | 30 | 150 |

B's one day work = | ||

150 |

Ratio of their income = | : | = 5 : 1 | |||||

30 | 150 |

∴ A's share = | × 5 = | × 5 = ₹ 2500 | |||||

( 5 + 1 ) | 6 |

B's share = | × 1 = | × 1 = ₹ 500 | |||||

( 5 + 1 ) | 6 |

**By formula ,**

Here, x = 30, y = 25 and a = 3000

Share of A = ₹ | = | = ₹ 2500 | |||||

x | 30 |

Share of B = ₹ | = | = ₹ 500 | |||||

x | 30 |

**Rule 4:** P, Q and R undertake to do a work for ₹ a. If together they do only x/y of the work and rest is done by R alone, then

Share of R = a | 1 - | ||||

y |

**Example:** A, B and C undertake to do a work for ₹ 600. A and B together do 1/3 of the work and rest is done by the C alone. How much should C get? **Solution**:-

Work done by ( A + B ) = | ||

3 |

Work done by C = 1 - | = | ||||

3 | 3 |

Ratio of incomes = | : | = 1 : 2 | |||||

3 | 3 |

∴ Share of C = | × 2 = | × 2 = ₹ 400 | |||||

( 1 + 2 ) | 3 |

**By formula,**Here, a = ₹ 600, x = 1 and y = 3

∴ Share of C = 600 | 1 - | = 600 × | = ₹ 400 | |||||

3 | 3 |

**Example:**A and B undertaken to do a piece of work for ₹ 1200. A alone can do it in 8 days, while B can do it in 6 days. with the help of C they complete it in 3 days. Find C's share.

**Solution**:-

Work done by ( A + B ) = | ||

3 |

Work done by C = 1 - | = | ||||

3 | 3 |

Ratio of incomes = ( A + B ) : c

Ratio of incomes = | : | = 1 : 2 | |||||

3 | 3 |

∴ Share of C = | × 2 = | × 2 = ₹ 400 | |||||

( 1 + 2 ) | 3 |

**By formula,**Here, a = ₹ 600, x = 1 and y = 3

∴ Share of C = 600 | 1 - | = 600 × | = ₹ 400 | |||||

3 | 3 |

A's one day work = | ||

8 |

B's one day work = | ||

6 |

C's one day work = | - | + | ||||||||

3 | 8 | 6 |

C's one day work = | - | - | ||||||

24 | 24 | 24 |

C's one day work = | - | = | ||||||

24 | 24 | 24 |

Ratio of their incomes = | : | : | = 3 : 4 : 1 | |||||||

8 | 6 | 24 |

∴ Share of C = | × 1 = | × 1 = ₹ 150 | |||||

( 3 + 4 + 1 ) | 8 |