Question

if the price of sugar is increased by 50% by how much percent a house wife must reduce the consumption of sugar so that her expenditure on sugar is increased by 20% only​

Answer 1

Answer: The consumption must be reduced by 20 %.

Step-by-step explanation:

Let the original price of sugar = x rupees per kg,

And, the consumption of the sugar = y kg,

⇒ Total original expenditure = xy rupees ( Expenditure × consumption )  

Now, the new price of the sugar = 50 % more than the original price

= 50 % more than x

= 150% of x

= 1.5 x

And, the new expenditure = 20% more than original expenditure

= 20% more than  xy

= 120% of xy

= 1.2 xy

Thus, the new consumption = New expenditure / New price

$=\frac{1.2 xy}{1.5 x}$

$=0.8y$

Hence, the percentage reduction in the consumption,

$=\frac{\text{Original consumption-New consumption}}{\text{Original consumption}}\times 100$

$=\frac{y-0.8 y}{y}\times 100$

$=\frac{0.2y}{y}\times 100$

$=20\%$

Therefore, the consumption must be reduced by 20 %.