Two numbers are in the ratio 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.
Given:
Two numbers are in the ratio 9 : 5.
9 is added to the greater number.
5 is subtracted from the smaller number.
The greater number becomes thrice the smaller number.
Solution:
Let the numbers be 9x and 5x, where x is a common factor.
According to the problem, 9x + 9 = 3(5x - 5)
15x - 9x = 9 + 15
6x = 24
x = 4
Greater number: 9x = 9 4 = 36
Smaller number: 5x = 5 4 = 20
Therefore, the numbers are 36 and 20.
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