Question

When the price of eggs is reduced by 20% it enables a man to buy 20 more eggs for Rs 40. Then the reduced price per egg is
(a) 38 paise
(b) 40 paise
(c) 42 paise
(d) 44 paise

Answer 1

Hint: In this question, you can assume that the original price per egg is Rs. x. Then, you can find the reduction in price by applying 20% on Rs. x. Using formula as the reduced price of each egg is equal to the original price per egg – the original price is reduced by 20 % per egg, you can find the final answer.

Complete step by step solution:
Let x be the original price per egg.
The number of eggs available for Rs. 40 = $\dfrac{40}{x}$
The original price of egg is reduced by $20\%=\dfrac{1}{5}$
The original price is reduced by 20% per egg = $\dfrac{x}{5}$
The reduced price of each egg = (The original price per egg ) $-$ (The original price is reduced by 20 % per egg)
The reduced price of each egg = $(x)-\left( \dfrac{x}{5} \right)=\dfrac{4x}{5}.........................(1)$
The number of egg available for Rs. 40 at the reduced rate =$\dfrac{40}{\left( \dfrac{4x}{5} \right)}=\dfrac{50}{x}$
 According the given condition,
(The number of egg available for Rs. 40 at the reduced rate) - (The number of eggs available for Rs. 40) = 20
$\left( \dfrac{50}{x} \right)-\left( \dfrac{40}{x} \right)=20$
$\dfrac{10}{x}=20$
$10=20x$
Dividing both sides by 20, we get
$x=\dfrac{10}{20}=\dfrac{1}{2}$
Now put this value in the equation (1), we get
The reduced price of each egg = $\dfrac{4x}{5}=\dfrac{4\times \dfrac{1}{2}}{5}=\dfrac{2}{5}=0.40$
Hence the reduced price of each egg is 40 paise.
Therefore, the correct option for the given question is option (b).

Note: You might get confused by the question, how do you take 20% of a price? First, convert the percentage discount to a decimal. A 20 percent discount is 0.20 in decimal format. Secondly, multiply the decimal discount by the price of the item to determine the savings in rupees. For example, if the original price of the item equals Rs. 40, you would multiply 0.2 by Rs.40 to get Rs. 8.