साखरेची किंमत 60% ने वाढली. घरात साखर किती टक्के कमी वापरावी म्हणजे खर्चात वाढ होणार नाही?

Given:

Increment on price of sugar = 60%

Formula Used:

Expenditure = Price × Consumption

Calculation:

Shortcut TrickIf the price of the commodity increases by R%, then % reduction in the consumption so as not to increase the expenditure is:

⇒ \([\frac{R}{(100 ~+~R)}× 100]\)%

Here, R = 60%

⇒ \([\frac{60}{(100 ~+~60)}× 100]\)% = \([\frac{60}{160}× 100]\)%

⇒ \([\frac{3}{8}× 100]\)% = 37​​​​\(\frac{1}{2}\)%

∴ The correct answer is 37​​​​\(\frac{1}{2}\)%.

Alternate Method

Let the price of sugar be Rs. x and its consumption be y.

Then, Expenditure = Price × Consumption

⇒ Expenditure = Rs. xy

According to the question, price of the sugar increased by 60%

Increased price = x + 60% of x = Rs. 1.6x

Expenditure remains the same = Rs. xy

Reduced consumption = Expenditure/Price = \(\frac{xy}{1.6x}\)

⇒ \(\frac{xy}{1.6x}\) = \(\frac{10y}{16}\) = \(\frac{5y}{8}\)% reduction in consumption

Reduction in consumption = \(\frac{y~-~\frac{5}{8}y}{y}\times 100\)

⇒ \([\frac{3}{8}× 100]\)% = 37​​​​\(\frac{1}{2}\)%

∴ The correct answer is 37​​​​\(\frac{1}{2}\)%.