Question

Q.1. A number is 6 more than the average of, its half, its one-third and its one-sixth. Find the number.

Answer 1

Dear student,


$$\begin{gathered} lettheno.bex \\ soaverageofits\frac{x}{3}and\frac{x}{6}=\frac{\frac{x}{3}+\frac{x}{6}}{2} \\ =\frac{2x+x}{12} \\ =\frac{3x}{12} \\ =\frac{x}{4} \\ Given:no.is6morethanitsaverage \\ \Rightarrow x-6=\frac{x}{4} \\ \Rightarrow x-\frac{x}{4}=6 \\ \Rightarrow \frac{4x-x}{4}=6 \\ \Rightarrow \frac{3x}{4}=6 \\ \Rightarrow x=\frac{6\times 4}{3} \\ \Rightarrow x=2\times 4 \\ \Rightarrow x=8 \\ Thustheno.is8 \end{gathered}$$

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