Out of nine persons,8 persons spent Rs. 30 ea | vedclass

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(C) Let the total expenditure of all $9$ persons be $S$.Then the average expenditure is $\frac{S}{9}$.Let the expenditure of the $9^{th}$ person be $x

Vedclass · Accepted Answer

$292.50$

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(C) Let the total expenditure of all $9$ persons be $S$.Then the average expenditure is $\frac{S}{9}$.Let the expenditure of the $9^{th}$ person be $x$.We know that $8$ persons spent $Rs. 30$ each,so their total expenditure is $8 	imes 30 = 240$.Thus,$S = 240 + x$.The average expenditure is $\frac{240 + x}{9}$.According to the problem,the $9^{th}$ person spent $Rs. 20$ more than the average:$x = \frac{240 + x}{9} + 20$Multiply the entire equation by $9$:$9x = 240 + x + 180$$9x - x = 420$$8x = 420$$x = 52.5$Now,the total expenditure $S = 240 + 52.5 = 292.5$.Therefore,the total money spent by all of them is $Rs. 292.50$.

Out of nine persons,$8$ persons spent $Rs. 30$ each for their meals. The ninth person spent $Rs. 20$ more than the average expenditure of all the nine. What was the total money spent by all of them (in $Rs.$)?

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