Due to a 20% fall in the prices of eggs, a man purchased 15 eggs more for rs. 45. Find the original and the reduced rates of eggs.
Answers
Let x be the original cost of the egg.
Let y be the number of eggs the man can buy.
Before the fall in price:
Number of eggs = Amount he has ÷ price of 1 egg
⇒ y = 45/x -------------------------- [ 1 ]
After the fall of the egg:
Price of the egg = 100 - 20 = 80%
Price of the egg = 80% x = 0.8x
Number of eggs he can buy :
⇒ y + 15 = 45/0.8x -------------------------- [ 2 ]
Put the 2 equations together :
y = 45/x -------------------------- [ 1 ]
y + 15 = 45/0.8x -------------------------- [ 2 ]
Equation [ 2 ] - [ 1 ]:
45/0.8x - 45/x = 15
(45 - 45(0.8))/ 0.8x = 15
9/0.8x = 15
(15) 0.8x = 9
12x = 9
x = 9 ÷ 12
x = Rs 0.75
Find the price of the eggs:
Before reduced = x = Rs 0.75
After reduced = 0.8x = 0.8(0.75) = Rs 0.60
Answer: The original price of the egg is Rs 0.75 and it becomes Rs 0.60 after reduction.