Question

A cricketer has a mean score of 58 runs in 9 innings. Find how many runs are to be scored in the 10th inning to raise his mean score to 61.

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Given},\mathrm{mean}\mathrm{score}\mathrm{in}9\mathrm{innings}=58 \\ \mathrm{we}\mathrm{know},\mathrm{mean}=\frac{\mathrm{total}\mathrm{value}}{\mathrm{total}\mathrm{count}}=\frac{\mathrm{x}+\mathrm{y}+\mathrm{z}....\mathrm{n}}{\mathrm{n}} \\ \mathrm{let}\mathrm{total}\mathrm{score}\mathrm{in}9\mathrm{innings}\mathrm{be}\mathrm{n} \\ \Rightarrow \frac{\mathrm{n}}{9}=58 \\ \Rightarrow \mathrm{n}=58\times 9=522 \\ \mathrm{Now},\mathrm{we}\mathrm{want}\mathrm{to}\mathrm{raise}\mathrm{the}\mathrm{mean}\mathrm{score}\mathrm{to}61\mathrm{in}10\mathrm{innings}, \\ \mathrm{let}\mathrm{the}\mathrm{score}\mathrm{in}10\mathrm{th}\mathrm{inning}\mathrm{be}\mathrm{x} \\ \Rightarrow \frac{522+\mathrm{x}}{10}=61 \\ \Rightarrow \mathrm{x}=610-522 \\ \Rightarrow \mathrm{x}=88 \\ \mathbf{the}\mathbf{}\mathbf{score}\mathbf{}\mathbf{in}\mathbf{}\mathbf{10}\mathbf{th}\mathbf{}\mathbf{inning}\mathbf{=}\mathbf{88} \end{gathered}$$

Regards