The family needs to reduce their consumption by 50% to keep their expenditure fixed.
To keep the expenditure fixed despite the increase in price, the family needs to adjust their consumption in proportion to the change in price. Here's how you can calculate the percentage reduction in consumption:
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First, let's calculate the initial expenditure and the new expenditure:
Initial expenditure = Initial price per kg * Initial consumption = Rs. 32/kg * X kg (where X is the initial consumption) = Rs. 32X
New expenditure = New price per kg * New consumption = Rs. 64/kg * Y kg (where Y is the new consumption)
Since the expenditure remains constant, we equate the initial expenditure to the new expenditure:
Rs. 32X = Rs. 64Y
Solving for Y, the new consumption:
Y = (32X) / 64 = X / 2
To find out the reduction in consumption as a percentage:
Reduction percentage = ((Initial consumption - New consumption) / Initial consumption) * 100 = ((X - Y) / X) * 100 = ((X - X/2) / X) * 100 = (X/2) / X * 100 = 50%
So, the family needs to reduce their consumption by 50% to keep their expenditure fixed.
Define Percentage Change
Percentage change is a measure used to express the difference between two values as a percentage of one of the values. It indicates how much a value has increased or decreased relative to its initial value.
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The formula for calculating percentage change is:
Percentage Change = ((New Value - Old Value) / Old Value) * 100%
Where:
- New Value is the updated or current value.
- Old Value is the original or previous value.
This formula calculates the difference between the new and old values, divides it by the old value, and then expresses it as a percentage by multiplying by 100. A positive percentage change indicates an increase, while a negative percentage change indicates a decrease.
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