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
∴ Daily wages = ₹ 180
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
Example: 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?
Solution:- Time taken by A = 5 days
Time taken by B = 7 days
Total amount earned = ₹ 7200
= 600 × 5 = ₹ 3000
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
Time taken by B = 6 days
Total incomes = ₹ 5500
= 500 × 6 = ₹ 3000
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
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
LCM of 3, 4 and 5 = 60
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
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:
Total income = ₹ 3000
By formula,
Here, x = 30, y = 25 and a = 3000
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
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:-
Total income = ₹ 600
Ratio of incomes = ( A + B ) : c
By formula,
Here, a = ₹ 600, x = 1 and y = 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:-
Total income = ₹ 600
Ratio of incomes = ( A + B ) : c
By formula,
Here, a = ₹ 600, x = 1 and y = 3
Total income = ₹ 1200
