Question

(14. The price of sugar goes up by 20%. By how much per cent must a house wife reduce her
consumption so that the expenditure does not increase?​

Answer 1

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The price of sugar goes up by 20%. By how much per cent must a house wife reduce her  consumption so that the expenditure does not increase?​

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The price of sugar goes up by $20$%.

$\huge\bold{{\pink{T}}{\blue{O}}{\green{  }}{\red{F}}{\purple{I}}{\orange{N}}{\pink{D}}{\green{❥}}}$

The percentage by which the house wife should reduce her consumption so that the expenditure does not increase.

$\huge\bold{{\pink{S}}{\blue{O}}{\green{L}}{\red{U}}{\purple{T}}{\orange{I}}{\pink{O}}{\blue{N}}{\green{❥}}}$

Let the consumption of sugar originally be 1 unit and let its cost be ₹ $100$.

Price increases by $20$%.

New price of sugar

= ₹ $120$

Now, ₹ $120$ yield $1$ unit of sugar.

∴ ₹ $1$ will yeild $(\frac{1}{120} )$ unit of sugar.

∴ ₹ 100 will yield $(\frac{1}{120} ×100)$ unit

                          = $\frac{5}{6}$ unit

Reduction in consumption×

= $(1-\frac{5}{6})$ unit

= $\frac{1}{6}$ unit

∴ Reduction % in consumption

= $(\frac{1}{6} × \frac{1}{1} ×100)$ %

= $\frac{50}{3}$ %

= $16\frac{2}{3}$ %

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Reduction % in consumption

= $16\frac{2}{3}$ %

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The house wife should reduce her consumption by $16\frac{2}{3}$ %  so that the expenditure does not increase.

$\huge\bold{{\pink{D}}{\blue{O}}{\green{N}}{\red{E}}{\purple{࿐}}}$

Answer 2

$\underline{ \underline{ \bf \large \pink{Solution}}}$


$\sf \: Let \: The \: Original \: price \: of \: sugar \: be = Rs. 100$



$\sf after \: increasing = 100 + 20 \% \: of \: 100$


$\to \: \: \: \sf 100 + \frac{20}{ \cancel{100}} \times \cancel{100} = Rs. 120 \:$



$\sf \:Reduction \: Rs. \: 120 = Rs. \: 20.$


$\: \: \: \: \: \: \: \: \: \: \color{red} \sf \: on \: Rs. 1 = \frac{20}{120}$


$\: \: \: \: \: \: \: \: \: \: \sf \color{red} on \: Rs. \: 100 = \frac{ \cancel{2}9}{1 \cancel{2}} \times 100 = \frac{100}{6} = \frac{50}{3}$




$\underline{ \underline{ \boxed{\sf \color{blue} \implies \: 16.66 \%}}}$