A man increases his consumption of sugar by 44.44% because the price of sugar is reduced by P%. Find P. (Expenditure remains constant.)

Correct option is A

Given:

A man increases consumption by 44.44%

Solution:

Let the price of sugar be Rs.100

And consumption be 100

Total expenditure = $100 \times 100$ = 10000

Consumption increased by 44.44% = $\frac{4}{9}$

New consumption = 100 + 44.44% of 100 = $\frac{1300}{9}$

Let the dropped price be $x$

Then, expenditure = $x \times \frac{1300}{9}$

But the expenditure is same in both cases;

Hence,

$x \times \frac{1300}{9}= 10000$

$x =\frac{10000\times 9}{1300}= \frac{900}{13}$

Price dropped = $100- \frac{900}{13}= \frac{1300-900}{13}$

$=\frac{400}{13}$

Percentage dropped = $\frac{\frac{400}{13}}{100} \times 100 = \frac{400}{13}\% =30\frac{10}{13}\%$

Alternate Method:

Consumption increases by 44.44% (i.e. $\frac{4}{9})$ .

Expenditure is constant.

With constant expenditure: ( $\text{Price factor}) \times (\text{Quantity factor}) =$ 1.

Price increase by P%.

Price factor = $1-\dfrac{P}{100}$ ; Quantity factor = 1 $+\dfrac{4}{9}=\dfrac{13}{9}$ .

$\left(1-\frac{P}{100}\right)\times\left(\frac{13}{9}\right)=1$
$1-\frac{P}{100}=\frac{9}{13}$

$\frac{P}{100}=1-\frac{9}{13}=\frac{4}{13}$

$P=\frac{400}{13}\%=30\frac{10}{13}\%$

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A man increases his consumption of sugar by 44.44% because the price of sugar is reduced by P%. Find P. (Expenditure remains constant.)

$30\frac{10}{13}\%$

$32\frac{10}{13}\%$

$20\frac{10}{13}\%$

$25\frac{10}{13}\%$

Correct option is A