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# The ratio of two numbers is 9:5. If 9 is added to the greater number and 5 is subtracted from the smaller number, the greater number becomes thrice the smaller one. Find the numbers.  Verified
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Hint: To solve this question, we multiply the ratio with a variable x. Then we make the necessary modifications to these numbers as given in the question. Then we solve for x to get the answer.

Given Data, the numbers are in a 9:5 ratio.

Multiply the ratios with x, then numbers become 9x and 5x.

So 9x is the greater number and 5x is the smaller number.

Given 9 is added to the greater number
i.e, 9x + 9

Given 5 is subtracted from the smaller number
i.e, 5x – 5

Now the numbers are 9x+9 and 5x -5

Given greater number becomes thrice the smaller one
i.e, 9x + 9 = 3(5x – 5)
=>9x + 9 = 15x -15
=> 6x = 24
=> x = 24/6
=> x = 4
Hence, the numbers are 9x and 5x i.e., 36 and 20.

Note: In such types of problems the key is to write the numbers given in the ratio, in the form of a variable like 9x and 5x. Making the modifications to these numbers using the sentences in the question is the next important step, it is easier to proceed with the problem this way. This way a relation is established, solve it for the answer.