Word Problem No.4 (Compound Proportion) --- Labourers, Time, and Earning (Compound Proportion among three quantities)

If 15 laboures earn Rs. 67,500 in 9 days, how much money will 10 laboures earn in 12 days? 

Solution: 

We see that as the number of labourers decrease, the amount of earning will also decrease. It is a direct proportion. 

As the working days increase, the amount of earning will also increase. It is also a direct proportion. 

Let the earning amount be ｘ Rs.

Here the equation will be 

`\frac{ｘ}{67,500}`  = `\frac{12}{9}` ｘ `\frac{12}{15}` 

Or

ｘ = `\frac{12}{9}` ｘ `\frac{12}{15}`  ｘ 67,500 Rs.

by simplifying we get

ｘ =  72,000 Rs.

Thus, Rs. 72,000 will be earned