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The ratio of three numbers is 17 : 19 : 22. If the first number is decreased by 24, the ratio of the first number to the third number will be 1 : 2. When the third number is increased by 7, the ratio of the second and the third number will be 4 : 5. Find the sum of the three numbers. 

The ratio of three numbers is 17 : 19 : 22. If the first number is decreased by 24, the ratio of the first number to the third number will be 1 : 2. When the third number is increased by 7, the ratio of the second and the third number will be 4 : 5. Find the sum of the three numbers.  Correct Answer 232

Given:

The ratio of three numbers is 17 : 19 : 22

If the first number is decreased by 24, the ratio of the first number to the third number will be 1 : 2

When the third number is increased by 7, the ratio of the second and the third number will be 4 : 5

Formula:

Average age of a group of n members: a1, a2, ..., an = (a1 + a2 + a3 + ... + an)/n

Calculation:

Let the 1st number be 17x, second be 19x and third be 22x

As per question

(17x – 24)/22x = 1/2

⇒ 34x – 48 = 22x

x = 4

Sum of 3 numbers = 17 × 4 + 19 × 4 + 22 × 4 = 68 + 76 + 88 = 232

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