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If the price of sugar is increased by $7%$, then by how much per cent should a housewife reduce the consumption of sugar, to have no excess expenditure

ATTEMPT

Let family consume $100$ units of sugar. Price of $1$ unit is $\$100$. Total expenditure is $\$10,000$.

Now new expenditure will be $\$10,700$.

So we have $700$ as extra expenditure. So units which are extra are $700/107$.

Hence we have to reduce consumption by $700/107=6.542\%$.

But textbook writes as $7/107$ percent. Can someone explain to me this? Am I wrong or textbook?

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Consumption needs to be reduced by an amount corresponding to $\dfrac{7}{107} \approx 0.06542$ of the original consumption.

Written as a percentage this would be $6.542\%$ which is $\dfrac{700}{107}\%$

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  • $\begingroup$ Oh my answer is correct that means $\endgroup$ – Taylor Ted Jul 25 '15 at 7:55
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Hint:

Let $E_1=p_1n_1$ the initial expenditure ($p_1$ is the initial price and $n_1$ is the initial quantity).

The new price is $p_2=p_1(1+0.07)$. You want: $p_1n_1=p_1(1+0.07)n_2$ and you can find: $\dfrac{n_2}{n_1}$.

The percent reduction is $1-\dfrac{n_2}{n_1}$

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We need $10700\times y=10000$, so $y=\dfrac{10000}{10700}=\dfrac{100}{107}=0.9346\dots$

As the original expenditure can be considered to be $1$, we need to reduce it by $1-0.9346\dots\%=0.0654\dots\%$

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