Question

Due to a 25% fall in the rate of eggs, one can buy 2 dozen eggs more than before by investing Rs. 162. Then the original rate per dozen of the eggs is
(1) Rs. 22
(2) Rs. 24
(3) Rs. 27
(4) Rs. 30

Answer 1

Hint: Let the original rate of eggs be $x$ per dozen. Then, find the number of dozens of eggs that can be bought from Rs. 162. Next, calculate the decreased price and find the number of eggs that can be bought. It is given that the person can buy 2 more dozens of eggs, hence, form the equation and solve for $x$

Complete step-by-step answer:
We are given that when the price of the eggs is decreased by 25% and now the person can buy 2 more dozens of eggs from Rs. 162
Let the initial price of the eggs be $x$ per dozen.
Then, the number of eggs can be bought from Rs. 162 can be calculated by dividing 162 from the price of eggs.
Then, the number of dozens of eggs are $\dfrac{{162}}{x}$
Then, the new price is 25% less than the original price which can be written as
$x - 25\% x$
Which can be simplified as,
$
  x - \dfrac{{25}}{{100}}x \\
   \Rightarrow x - \dfrac{1}{4}x \\
   \Rightarrow \dfrac{{4x - x}}{4} \\
   \Rightarrow \dfrac{{3x}}{4} \\
$
Hence, the new price of the eggs is $\dfrac{{3x}}{4}$ per dozen.
Hence, number of dozens eggs of that can be bought from Rs. 162 is $\dfrac{{162}}{{\dfrac{{3x}}{4}}} = \dfrac{{216}}{x}$
Also, we are given that the person can buy 2 more dozens of eggs, that is,
$
  \dfrac{{216}}{x} - \dfrac{{162}}{x} = 2 \\
   \Rightarrow \dfrac{{54}}{x} = 2 \\
$
On cross- multiplying , we get,
$54 = 2x$
Dividing the equation throughout by 2
$x = 27$
Therefore, the original price of eggs per dozen is Rs. 27
Hence, option C is correct.

Note: The price of egg and the number of dozens of eggs bought is equal to the price given. Use the relation to find the number of eggs for each rate. Form the equations correctly and avoid calculation mistakes in these types of questions. Also, 25% can be written as $\dfrac{{25}}{{100}}$.