There are some problems which involve the sharing of money between men for completing a work. In these problems, it is generally assumed that the money is shared by the men in the ratio of the work completed by each of them. This ratio of work done depends on their individual rates of doing work and also the number of days for which they worked. i.e., if the ratio of work done by two persons is a : b, then the ratio of money shared between them is also in the ratio a : b.
The efficiency of work is the work rate, i.e., the work done in unit time. If the efficiency of a person is twice that of another, the first person can do twice the quantity of work that the second person does in a given time.
Equating Men, Women and Children
This is derived from the concept of efficiencies. It is generally assumed that the efficiencies of men, women and children are all different. Hence, if ‘x’ men can do certain work in ‘y’ days and ‘p’ women can do the same work in ‘q’ days, the work done is ‘x × y’ man-days or ‘p × q’ woman- days. Since the amount of work done in each case is the same, the two can be equated,
i.e., xy = pq, or 1 man-day = pq/xy woman-days.