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If the price of sugar is raised by 25%, find by how much per cent a householder must reduce his consumption of sugar so as not to increase his expenditure?1). 102). 203). 184). 25 |
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Answer» Let the initial consumption of sugar be Y units and the initial price of sugar PER KG be Rs. X. Thus, The initial expenditure of household = X × Y Given: the price of sugar increased by 25%. Thus, ⇒New price of sugar per kg $( = X + \frac{{25}}{{100}}X)$ = 1.25X Let the new consumption to keep the expenditure same be Y’ units. Hence, New expenditure = 1.25X × Y’ Since the EXPENDITURES are same, ∴ XY = 1.25XY’ ⇒ Y = 1.25Y’ Also, Reduction in consumption = Y – Y’ = 1.25Y’ – Y’ = 0.25Y’ ⇒ Reduction percentage $(= \frac{{Y - Y'}}{{Y}} \times 100)$ $( = \frac{{1.25Y' - Y'}}{{1.25Y'}} \times 100)$ = 20% |
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