Final answer:
To find the ratio between the reduction in consumption and the original consumption when the price of sugar is increased by 20%, we can use the equation x - y = 0.8x, where x represents the original consumption and y represents the reduction in consumption. The ratio is 1:5.
Step-by-step explanation:
To find the ratio between the reduction in consumption and the original consumption, we need to understand the concept of percentage increase and decrease. Let's assume the original consumption of sugar is represented by 'x'. When the price of sugar is increased by 20%, the new price becomes 120% of the original price, which can be calculated as 1.2x.
Now, if the expenditure is not allowed to be increased, the consumer would have to reduce their consumption to maintain the same total expenditure. Let the reduction in consumption be represented by 'y'. The new consumption can be calculated as x - y. Therefore, the ratio between the reduction in consumption and the original consumption is y : x. We need to find the value of y/x.
Since the price has increased by 20% and the consumer is not allowed to increase their expenditure, the new consumption must be lower than the original consumption. So, we can write the equation as:
x - y = 0.8x
Simplifying the equation,
0.2x = y
Therefore, the ratio between the reduction in consumption and the original consumption is 0.2x : x or simply 1 : 5.
Therefore answer is (b) 1:5.