Word Problem 14

Problem 14: If the price of sugar can be raised by 20%, the percentage of consumption that a house wife has to decrease in order not to increase her expenditure is;

a. 16-2/3%            b. 75%        c. 80%            d. 20%

— discrete math, business math —

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Solution:

 

 

We are given information as;

Increase in price of sugar = 20%

Reduction in consumption = ?

Expenditure = Same

Let initial price of sugar per kg is Rs 100 and consumption is also 100 kg. Then we arrange data as under;

Status of Price of Sugar Price amount Consumption Expenditure
Original

New (after 20% increase)

100

120

100 kg

?

100×100= Rs 10000

Rs 10000 (same as old)

Her we use a formula for new consumption;

New Consumption = \frac{Expenditure}{New Price}

= \frac{10000}{120}= 83\frac{1}{3} kg

With original price the consumption is 100 kg – now to find the difference of consumption after keeping expenditure same (Rs 10000), we subtract new consumption from original consumption;

\Rightarrow Reduction In Consumption = Original Consumption -New Consumption

\Rightarrow Reduction In Consumption = 100-83\frac{1}{3}

\Rightarrow Reduction In Consumption = 16\frac{1}{3} kg

Now to find the reduction percentage we use’

Reduction %age = \frac{New Consmp.}{Old Consmp}\times100

 \Rightarrow Reduction %age = \frac{16\frac{1}{3}}{100}\times100

 \Rightarrow Reduction %age = 16\frac{1}{3}}%

 


					
					
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