Question

A group of 3 friends staying together, consume 54 kg of wheat every month. Some more friends join this group and they find that the same amount of wheat lasts for 18 days. How many new members are there in this group now?

Answer 1

Let x be the number of new members in the group.

Number of members	3	x
Number of days	30	18

$$\begin{gathered} \mathrm{Since}\mathrm{more}\mathrm{members}\mathrm{can}\mathrm{finish}\mathrm{the}\mathrm{wheat}\mathrm{in}\mathrm{less}\mathrm{number}\mathrm{of}\mathrm{days},\mathrm{it}\mathrm{is}\mathrm{a}\mathrm{case}\mathrm{of}\mathrm{inverse}\mathrm{variation}. \\ \mathrm{Therefore},\mathrm{we}\mathrm{get}: \\ 3\times 30=x\times 18 \\ \Rightarrow 90=18x \\ \Rightarrow x=\frac{90}{18} \\ \mathrm{Thus},\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{new}\mathrm{members}\mathrm{in}\mathrm{the}\mathrm{group}=5-3=2 \end{gathered}$$