By what quantity the use of coal is to be reduced to keep one’s family budget same when the price of coal is increased by 50%?
Correct Answer: Option C
Let the initial coal used by family be denoted by X units and the initial cost of coal be Rs. Y per unit.
Hence, initial expenditure of family = Rs. XY
According to question, New cost of coal per unit = Y + 0.5Y
= Rs. 1.5Y
Let the new consumption of coal be X’.
∴ New expenditure = Rs. 1.5YX’
Since, the expenditure has to be same, hence
⇒ XY = 1.5X’Y
\(\Rightarrow X' = \frac{X}{{1.5}}\)
∴ Change in consumption = X – X’
\(= X - \frac{X}{{1.5}}\)
= X/3
Hence, percentage change in consumption reduced
\(= \frac{{\frac{X}{3}}}{X} \times 100\)
= 33.33%
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