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The sum of two numbers is 2490. If 6.5% of one number is equal to 8.5% of the other, find the numbers.

The sum of two numbers is 2490. If 6.5% of one number is equal to 8.5% of the other, find the numbers.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
11 months ago
Let's assume the first number is x and the second number is y. According to the problem, the sum of the two numbers is 2490, so we have the equation: x + y = 2490 ---(equation 1) Now, it is given that 6.5% of one number is equal to 8.5% of the other. Mathematically, we can express this as: 0.065x = 0.085y To solve this equation, we can rewrite it as: x = (0.085/0.065)y Now, substitute this value of x in equation 1: (0.085/0.065)y + y = 2490 Simplify the equation: (0.085y + 0.065y) / 0.065 = 2490 Combine like terms: 0.15y / 0.065 = 2490 Simplify further: y = (2490 * 0.065) / 0.15 y ≈ 1074 Now substitute the value of y back into equation 1 to find x: x + 1074 = 2490 x ≈ 1416 Therefore, the two numbers are approximately 1416 and 1074.

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