Correct Answer - Option 2 : 2240
Given:
Ratio of numbers = 5 ∶ 7
Number subtracted from each number = 8
New ratio of numbers = 2 ∶ 3
Calculation:
Let the numbers be x and y respectively, then
x ∶ y = 5 ∶ 7
⇒ x = 5y/7 ----(1)
According to the question
(x - 8) ∶ (y - 8) = 2 ∶ 3
⇒ (x - 8) × 3 = (y - 8) × 2
⇒ 3x - 24 = 2y - 16
⇒ 3x - 2y = 8
⇒ 3(5y/7) - 2y = 8 ----[From equation (1)]
⇒ 15y - 14y = 8 × 7
⇒ y = 56
And, x = (5 × 56)/7
⇒ 40
Product of numbers = 56 × 40
⇒ 2240
∴ The product of two numbers is 2,240.
