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: To solve this question, we will assume that the number of eggs the man buy before the price reduction be n and the price of each egg is Rs. x. After price reduction, the number of eggs he buys will be obtained by the data given in the question. On the basis of this, we will form two equations in two variables and then solve it by substitution method.

Complete step-by-step answer:
In the question, it is given that a man buys a certain number of eggs before the price reduction. Let him buy ‘n’ number of eggs before price reduction. Let the price of each egg be Rs. x before price reduction. It is given in the question that the total cost of all the eggs is Rs. 40. The total cost will be obtained by multiplying the cost of one egg to the number of eggs. Thus, we have,
\[n\times x=40\]
\[\Rightarrow nx=40.....\left( i \right)\]
Now, we are given that after the price reduction, the man can buy 20 more eggs. Thus, the total number of eggs he will be able to buy now is (n + 20). The reduced price of each egg is 20 % less than the original price. So, the new price is 80 % of the original. Thus the reduced price is given by:
Reduced price = 80 % of the original
Reduced price = \[\dfrac{80}{100}\times x\]
Reduced price = \[\dfrac{80x}{100}\]
Now, the total cost of all the eggs he can buy is Rs. 40. Thus, we will get the following equation:
\[\left( n+20 \right)\times \left( \dfrac{80x}{100} \right)=40\]
\[\Rightarrow \left( n+20 \right)\times \left( \dfrac{80x}{100} \right)=40\]
\[\Rightarrow \dfrac{80}{100}\left( nx \right)+\dfrac{20\times 80x}{100}=40.....\left( ii \right)\]
Now, we will substitute the value of nx from (i) to (ii). After doing this, we will get,
\[\Rightarrow \dfrac{80}{100}\left( 40 \right)+\dfrac{20\times 80x}{100}=40\]
\[\Rightarrow 32+16x=40\]
\[\Rightarrow 16x=40-32\]
\[\Rightarrow 16x=Rs.8\]
x = Rs. 0.5
\[x=0.5\times \left( 100\text{ paise} \right)\]
x = 50 paise
Now, the reduced price will be \[=\dfrac{80x}{100}\]
Reduced price \[=\dfrac{80}{100}\left( 50\text{ paise} \right)=40\text{ paise}\]
Hence, option (b) is the right answer.

Note: Another way of solving the above question is shown below: Let the reduced price be Rs. y. Now, it is given that the price is reduced by 20 %. The reduction in price \[=\dfrac{20}{100}\times 40=Rs.8.\] With Rs 8, now the man can buy 20 eggs of reduced price. Thus,
Reduced price of 20 eggs = Rs. 8
Reduced price of 1 egg \[=\dfrac{Rs.8}{20}=Rs.0.4=40\text{ paise}\]