Question

The Price of Sugar is increased by 50/3% and the consumption of a family is decreased by 20 %. Find the % change in his expenditure. ​

Answer 1

Answer:

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Step-by-step explanation:

Change in expenditure =increasepercentvalue−decreasepercentvalue−

100

increasepercentvalue×decreasepercentvalue

⇒20−25−

100

20×25

=20−30=−10

Hence expenditure will decrease by 10%

Answer 2

The percentage of change in his expenditure = 20/3 %

Given:

The Price of Sugar is increased by 50/3%  

the consumption of a family is decreased by 20 %

To find:

What is the percentage change in his expenditure

Solution:

Let the cost of sugar is Rs. x, and the consumption of a family is y kgs

=> Initial expenditure on sugar = Rs. x × y kg = xy Rs

The family spent Rs. xy on sugar initially

Given that Price of sugar is increased by (50/3) %

Then the price increased price on Rs. x = (50/3)% of x

= $\frac{\frac{50}{3} }{100} (x)$ = $\frac{50}{3} (\frac{1}{100} )(x)$ = $\frac{50x}{300} = (\frac{5x}{30} )$  

The final price of sugar after increasing the price will be

= $x+ \frac{5x}{30}$  = $\frac{35x}{30}$ = $\frac{7x}{6}$  

The final price of sugar = $\frac{7}{6} x$

Given that family, consumption decreased by 20%

=> decrease in consumption = 20% of y = $\frac{20}{100} y$ = $\frac{1}{5} y$  

Amount of consumption after decreasing = $y - \frac{1}{5} y = \frac{4}{5} y$  

Consumption of sugar after decreasing consumption = 4/5 y  

Then the expenditure on sugar after increasing the price

= $\frac{7}{6} x (\frac{4}{5} )y$ = $(\frac{28}{30} )xy$ = $\frac{14}{15} xy$      

The final expenditure on sugar after increasing the price = 14/15xy  

Change in expenditure = Initial expenditure - final expenditure

=  $xy - \frac{14}{15} xy$ = $\frac{15 xy - 14xy }{15}$ = $\frac{ xy }{15}$  

The percentage of chage = $\frac{xy}{15} (\frac{1}{xy} ) \times 100$ = $\frac{100}{15}$ = $\frac{20}{3}$%

Therefore,

The percentage of change in his expenditure = 20/3 %

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