**Quantitative Aptitude Work and Wages Study Material**

The wage earned by a worker is directly proportional to the amount of work he does. As discussed in the previous chapter, the amount of work done by a person depends on his efficiency and time spent. Efficiency is inversely proportional to the time taken to do the work. Thus, wages are distributed in direct proportion to the amount of work done by individual workers.

Total wage earned by a group of persons is given by (assuming equal efficiency for each person),

Total wage = One person’s one day’s wage x Number of persons x Number of days.

**Ex. 1. A can do a work in 10 days while B can do it in 8 days. Both of them work together to do the work. If the total amount paid for the work is Rs. 180, how much is A’s share in it?**

**Sol**. A’s daily work = 1/10

B’s daily work = 1/8

When working together, the total amount of work done by each of them will be in the same ratio as their daily work. And hence the ratio of their wages will be also in the ratio of their daiily work. ‘

.’. Ratio of their wages

A:B = 1/10:1/8

.’. A’s Share = (4/4+5) x Rs. 180 = Rs. 80

Note : When all the members of a group working to¬gether spend equal time to do a piece of work, the total wage is distributed in direct proportion to the working capacity of individual members. In other words, the total wage is distributed in inverse proportion to the time taken by the individual members to do the job separately.

**Ex. 2. A can do a certain piece of work in d, days and B in d2 days. Both of them work together to do the work. If the total amount paid for the work is Rs. M, how much would each get?**

Sol. A’s daily work = 1/d1

B’s daily work = 1/d2

The amount of work done by them will be in the same ratio as their daily work because both of them work together for the same time period. And hence, the ratio of their wages will also be the same as ratio of their daily works.

A’s share : B’s share 1/d1: 1/d2 = d2:d1

Note : Ratio of wages is in inverse proportion to the time taken by them to do the work alone.

**Ex. 3. A, B and C can do a work in 8, 12 and 20 days respectively. They finish the work together and earn Rs. 620. What is the share of each?**

Sol. A’s share : B’s share : C’s share = 1/8 : 1/12 : 1/20

Multiplying each ratio by the LCM of their denominators it becomes

120/8: 120:12:150/20 = 15:10:620

**Ex. 4. A, B and C can do a piece of work in d1d2 and d3 days respectively. If they work together, in what proportion should their total earnings be divided amongst them?**

**Sol.** A’s daily work = 1/d1

B’s daily work = 1/d2

C’s daily work = 1/d3

Since they are working together for equal time, the amount of work done by each will be in proportion to their daily work and so will be their shares in the total earnings.

A’s share : B’s share : C’s share = 1/d1: 1/d2:1/d3

Multiplying each term in the ratio by (d1d2d3)

= d2d3 :d1d3 :d1d2

A’s share : B’s share : C’s share = d2d3: d1d3 : d1d2 Note : It is easy to remember if you notice A’s time (i.e., d1) is missing from the term corresponding to A’s share and so on.

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