The sum of two numbers is 456. If the bigger number is decreased by 20% and the smaller number is increased by 10%, then the numbers obtained are equal. The smaller number is-

Question: The sum of two numbers is 456. If the bigger number is decreased by 20% and the smaller number is increased by 10%, then the numbers obtained are equal. The smaller number is-

Solution:
Let,
Larger number = x and smaller number = 456 - x

According to the question
⇒ 80x/100 = {(456 - x)/100} × 110
⇒ 80x = (456 - x) × 110
⇒ 80x = 456 × 110 - 110x
⇒ 110x + 80x = 456 × 110
⇒ 190x = 456 × 110
⇒ x = (456 × 110)/190
⇒ x = 264

∴ Smaller number = 456 - 264 = 192