A rise of 25 % in the price of sugar, compels a man to buy 5 kg sugar less for Rs. 200. The original price per kg of the sugar is $Rs .$ ____ .

Question

A rise of 25 % in the price of sugar, compels a man to buy 5 kg sugar less for Rs. 200. The original price per kg of the sugar is Rs. ____ .

Accepted Answer

Concept- We'll first presume the initial price of the sugar in the aforementioned query to be a variable. We will also consider the initial sugar content to be a variable. We will compare the initial cost to the new cost because the overall cost is unchanged.
Assume that the price of the sugar was Rs. C/kg at the time of purchase.
Since it is a known that the price of sugar has increased by

25 % .

Therefore, the new cost is equivalent to a

25 %

increase in the original cost.
New price,

(C + 25 %) = (C + \frac{25}{100} C) = (C + \frac{1}{4} C) = \frac{5}{4} C

Now consider the case when x kg of sugar was initially purchased.
Given that the man purchases

5 kg

less sugar,
New amount of sugar then equals

(x - 5) kg .

Additionally, the initial price of sugar is equal to Rs. (Cx).
New cost of sugar = new amount × new cost

= (x - 5) \times \frac{5}{4} C = Rs . \frac{5}{4} C (x - 5)

Given that we are aware that the overall cost is unchanged, we have the following:

C \times x = \frac{5}{4} C (x - 5)

The overall cost, which has also been disclosed, is Rs. 200.

C \times x = \frac{5}{4} C (x - 5) = 200 . . . . (1)

Now take into account

Cx = \frac{5}{4} C (x 5) .

\Rightarrow Cx = \frac{5}{4} Cx - \frac{25}{4} C s .

We obtain the following by adding 254C to the left of the equal sign:

Cx + \frac{25}{4} C = \frac{5}{4} Cx

Once more, if we move the term "Cx" to the right of the equal sign, we obtain the following:

\frac{25}{4} C = \frac{5}{4} Cx - Cx

\frac{25}{4} C = Cx (\frac{5}{4} - 1)

\frac{25}{4} C = Cx (\frac{5 - 4}{4})

\frac{25}{4} C = C x \times \frac{1}{4}

The result of multiplying the aforementioned equation by four is as follows:

\frac{25}{4}

c =

\frac{cx}{4}

25C = Cx
Equation tells us that the value of C x is 200, by putting it in equation we get that,
25C = 200
C =

\frac{200}{25}

C = 8 Rs/kg
Therefore,

Rs . 8

was the initial cost per kilogramme of sugar.
Hence, the current answer is

Rs . 8

.

A rise of 25 % in the price of sugar, compels a man to buy 5 kg sugar less for Rs. 200. The original price per kg of the sugar is $Rs .$ ____ .

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