Which of the following pair of symbols will define the

Solution

Quantity-I: A number is increased by 20%. If the new number is 240, find the original number. Quantity-II: A second number is decreased by 10%. If the new number is 180, find the original number. Quantity-III: A third number is increased by 15%. If the original number is 150, find the new number. Solution: Quantity I: Let the original number be x. x + 20% of x = 240 x + (20/100) × x = 240 x × (1 + 0.2) = 240 1.2x = 240 x = 240 / 1.2 = 200 Quantity II: Let the original number be y. y - 10% of y = 180 y - (10/100) × y = 180 y × (1 - 0.1) = 180 0.9y = 180 y = 180 / 0.9 = 200 Quantity III: New number = 150 + 15% of 150 New number = 150 + (15/100) × 150 New number = 150 + 22.5 = 172.5 Comparing Quantity-I, Quantity-II, and Quantity-III: Quantity-I = 200 Quantity-II = 200 Quantity-III = 172.5 Now, comparing: Quantity-I = Quantity-II Quantity-II > Quantity-III Therefore, the correct pair of symbols is: A & B Correct answer: a