Question

A batsman makes a score of 95 runs in the 13th match and thus increases his average runs per match by 4. What is his average after the 13th match?

Answer 1

Refer the attachment.

Answer 2

Question:-

A batsman makes a score of 95 runs in the 13th match and thus increases his average runs per match by 4. What is his average after the 13th match?

Solution:-

given :-

a) A batsman makes a score of 95 runs in the 13th match

b) increases his average runs per match by 4.

To find :- Average after the 13th match?

$\fcolorbox{red}{white}{before \:13th \: match \: let \: averge \: be \: x \: } \\ \\ \frac{\huge{x} \small{1} + \huge{x} \small{2} + ......+ \huge{x} \small{12}}{12} = \huge{ x} \\ \\ \huge{x} \small{1} + \huge{x} \small{2} + ......+ \huge{x} \small{12} = \huge{ 12 \: x} \: \: \: \: .....(1) \\ \\ \fcolorbox{red}{white} {after \: 13th\: match \: let \: avrage \: be \:( x + 4)} \\ \\ \frac{\huge{x} \small{1} + \huge{x} \small{2} + ......+ \huge{x} \small{12} + 95}{13} = \huge{ (x \: + 4)} \\ \\ \huge{x} \small{1} + \huge{x} \small{2} + ......+ \huge{x} \small{12} + 95 = \huge{13 (x \: + 4)} \\ \\ \red{now \: form \: {eq}^{n} (1)} \: \\ \\ = > 12x + 95 = 13x + 52 \\ \\ = > 95 - 52 = 13x - 12x \\ i.e. \\ \\ = > 13 - 12x = 95 - 52 \\ \\ = > x = 43 \\ \\ now \: put \: value \: of \: x \: in \\ \\ = >( x + 4) = 43 + 4 = 47 \\ \\ \fcolorbox{red}{white}{hence \: average \: after \: 13th \: match \: is \: 47. }\\ \\ \fcolorbox{red}{white}{i \: hope \: it \: helps \: you.}$