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Of three positive numbers, the ratio of the first and the second is 5 : 2, the ratio of the second and the third is 5 : 4. The product of the first and the third is 1800. What is the sum of the three numbers?

Of three positive numbers, the ratio of the first and the second is 5 : 2, the ratio of the second and the third is 5 : 4. The product of the first and the third is 1800. What is the sum of the three numbers? Correct Answer 129

The ratio of first and second number = 5 ∶ 2 = 25 ∶ 10

Ratio of second and third number = 5 ∶ 4 = 10 ∶ 8

Ratio of three number = 25 ∶ 10 ∶ 8

Let three numbers be 25a, 10a and 8a

Product of first and third number = (25a) × (8a) = 200a2

According to the question,

⇒ 1800 = 200a2

⇒ a2 = 9

⇒ a = 3

Now,

∴ Sum of all numbers = 25a + 10a + 8a = 43a = 43 × 3 = 129

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