Question

The ratio of two numbers is 9:5.If 9 is added to the greatest number and 5 is subtracted from the smaller number, the greater number becomes thrice the smaller number. Find the numbers with steps

Answer 1

Step-by-step explanation:

Let the numbers in the ratio 3 : 5 be 3x and 5x

If 9 subtracted from each of them, the numbers becomes 3x - 9 and 5x - 9

When 9 subtracted from 3x and 5x, the ratio of the numbers becomes 12 : 23.

According to the question,

\dfrac{3x - 9}{5x - 9} = \dfrac{12}{23}

23(3x - 9) = 12(5x - 9)

69x - 207 = 60x - 108

69x - 60x = 207 - 108

9x = 99

x = 99/9

x = 11

1st number => 3x

=> 3 * 11

=> 33

2nd number => 5x

=> 5 * 11

=> 55

∴ The smaller number is 33 and the bigger number is 55 respectively.