The sum of two numbers is 4500. If 10% of one number is 12.5% of the other, find the numbers.

The sum of two numbers is 4500.

Let the number be x. The other number is (4500 - x).

So, 10% of one number is 12.5% of the other number.

10% of x = 12.5% of (4500 - x)

$⇒ \dfrac{10}{100} \times x = \dfrac{12.5}{100} \times (4500 - x)\\[1em] ⇒ \dfrac{x}{10} = \dfrac{125}{1000} \times (4500 - x)\\[1em] ⇒ \dfrac{x}{10} = \dfrac{(4500 - x)}{8} \\[1em]$

By cross multiplying, we get :

⇒ 8x = 10(4500 - x)

⇒ 8x = 45000 - 10x

⇒ 8x + 10x = 45000

⇒ 18x = 45000

⇒ x = $\dfrac{45000}{18}$

⇒ x = 2500

Other number = (4500 - x)

= (4500 - 2500)

= 2000

Hence, the two numbers are 2500 and 2000.