A set of numbers has the sum ' $S$ '. Each number of the set is increased by $20$ , then multiplied by $5$ , and then decreased by $20$ . The sum of the numbers in the new set thus obtained is:

S + 20 n

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5 S + 80 n

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5 S + 4 n

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5 S

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Solution

The correct option is D $5 S + 80 n$
Suppose there are $n$ numbers in a set
$x_{1} + x_{2} + . . . . . . + x_{n}$ , then
$x_{1} + x_{2} + . . . . . + x_{n} = S$
$\Rightarrow 5 (x_{1} + 20) - 20 + 5 (x_{2} + 20) - 20 + . . . . . + 5 (x_{n} + 20) - 20$
$\Rightarrow 5 (x_{1} + x_{2} + . . . . . + x_{n}) + 80 + 80 + . . . . + 80 n$ times
$\Rightarrow 5 S + 80 n$
Hence, option 'B' is correct.

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