Question

In a school , there are as many children in each room as thrice the number of rooms in the school. For charity, each child contributes an average amount of Rs 16/3. If the total money contributed was Rs 25600, then the number of children in each room of the school is.?

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{rooms}\mathrm{be}\mathrm{x} \\ \mathrm{then}\mathrm{number}\mathrm{of}\mathrm{children}=3\mathrm{x} \\ \mathrm{A}.\mathrm{T}.\mathrm{Q} \\ \mathrm{Total}\mathrm{money}\mathrm{contributed}=5\frac{1}{3}\left(\mathrm{Number}\mathrm{of}\mathrm{children}\right)\times \left(\mathrm{number}\mathrm{of}\mathrm{Rooms}\right) \\ 25600=\frac{16}{3}\left(3\mathrm{x}\right)\left(\mathrm{x}\right) \\ \Rightarrow {\mathrm{x}}^2=1600 \\ \Rightarrow \mathrm{x}=\pm 40 \\ \mathrm{since}\mathrm{number}\mathrm{of}\mathrm{rooms}\mathrm{cannot}\mathrm{be}\mathrm{negative}\mathrm{so}\mathrm{x}=40 \\ \mathrm{So}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{chldren}=3\times 40=120 \end{gathered}$$
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