Question

If the price of potatoes is reduced by 25 %, one can buy 6.25 kg more for Rs. 100. The reduced price of potatoes is
(a) Rs. 3 per kg
(b) Rs. 3.50 per kg
(c) Rs. 4 per kg
(d) Rs. 4.50 per kg

Answer 1

Hint: First of all, find the value of 25 % of Rs. 100 which would be the price of 6.25 kg potatoes. Now, as 6.25 kg potatoes is equal to 25 % of Rs. 100, so use the unitary method to find the value of 1 kg potatoes.
Complete step-by-step answer:
We are given that if the price of potatoes is reduced by 25 %, one can buy 6.25 kg more for Rs. 100. We have to find the reduced price per kg of potatoes. We are given that the price of potatoes is reduced by 25 %. So, there would be a saving of 25 % on Rs. 100, so we get,
Saving on Rs.100 due to the reduction of price = 25 % of Rs. 100
We know that x % of A is given by \[\dfrac{xA}{100}\]. By using this, we get,
Saving on Rs.100 due to reduction of the price \[=\dfrac{25\times 100}{100}=Rs.25\]
Due to the reduction of the price of potatoes by 25 % or saving of Rs. 25 on Rs. 100, one can buy 6.25 kg more potatoes that mean, the price of 6.25 kg potatoes is Rs. 25. So, we get,
Price of 6.25 kg potatoes = Rs. 25
By the unitary method, we get, price of 1 kg potatoes
\[=\dfrac{\text{Price of 6}\text{.25 kg potatoes}}{6.25\text{kg}}\]
\[=\dfrac{Rs.25}{6.25kg}\]
= Rs. 4 / kg
So, we get the reduced price of 1 kg potatoes as Rs. 4 / kg
Hence, the option (c) is the right answer.

Note: In this question, students can cross-check their answer as follows:
As the reduced price is Rs 4 per kg, for Rs. 100, one can buy \[=\dfrac{Rs.100}{Rs.4\text{ per kg}}=25kg\].
Let the initial price per kg be x. After reducing it by 25 %, it is equal to Rs. 4 / kg. So, we get,
x – 25 % of x = 4
\[x-\dfrac{x25}{100}=4\]
\[x-\dfrac{x}{4}=4\]
\[\dfrac{3x}{4}=4\]
\[x=Rs.\dfrac{16}{3}/kg\]
Initial price = \[Rs.\dfrac{16}{3}/kg\]
For Rs 100, one can buy \[=\dfrac{Rs.100}{Rs.\dfrac{16}{3}/kg}=18.75kg\] earlier.
So, the difference in quantities = 25 kg – 18.75 kg = 6.25 kg which is given in the question. So, our answer is correct.