Question

The price of sugar having risen by 50% by what fraction must a house holder reduce his consumption of sugar as not to increase his expenditure
(a) \[\dfrac{1}{4}\]
(b) \[\dfrac{1}{3}\]
(c) \[\dfrac{1}{2}\]
(d) \[\dfrac{2}{3}\]

Answer 1

Hint: To solve this question first of all assume x kg of sugar is of Rs.100. Using the 50% increase the sugar fact goes for making a new equation in the above assumed variable. It will give us a new cost of x kg of sugar. Then use the unitary method to get the kg of sugar of Rs.100. Finally, reduction in consumption can be obtained by subtracting old consumption to that of new consumption.

Complete step-by-step solution:
Let the consumption of sugar in that household be x kg and let us suppose that the price of sugar of x kg is Rs.100.
Let this be called the old price of sugar.
Now as the price of sugar is increased by 50%.
Therefore the new price of x kg sugar = old price of x kg sugar + \[\dfrac{50}{100}\] (old price of sugar)
\[\Rightarrow \] The new price of x kg sugar = 100 + \[\dfrac{50}{100}\] (100)
\[\Rightarrow \] The new price of x kg sugar = Rs.150.
So now we are getting x kg of sugar in 150Rs.
\[\Rightarrow \] For Rs.150 we get x kg of sugar.
Applying the unitary method \[\Rightarrow \]
For 1Rs. we get \[\dfrac{x}{150}\] kg of sugar.
So, for 100Rs. we get \[\dfrac{x}{150}\times 100\] kg of sugar.
\[\Rightarrow \] For 100Rs. we get \[\dfrac{2x}{3}\] kg of sugar.
So, originally we were having x kg of sugar in Rs.100 and now we are getting \[\dfrac{2x}{3}\] kg of sugar in Rs.100.
\[\therefore \] The reduction in consumption of sugar = old – new
\[\Rightarrow \] Reduction in consumption of sugar = \[x-\dfrac{2x}{3}\].
Taking LCM and solving we get,
Reduction in consumption of sugar = \[\dfrac{3x-2x}{3}=\dfrac{x}{3}\].
Therefore the householder should reduce the consumption of sugar to \[{{\dfrac{1}{3}}^{rd}}\] path.
So, option (b) is correct.

Note: Students can proceed to make mistakes at the point of assuming variable ‘x’. Never go for calculating the value of variable x. This step is not required as we need to find the relative reduction and nor the actual value. Hence we can easily proceed without calculating the value of variable x.