If three times the larger of two numbers is divided by the smaller, we get 4 as the quotient and 8 as the remainder. If five times the smaller is divided by the larger, we get 3 as the quotient and 5 as the remainder.

Find the numbers.

Let the Larger number be x and the smaller number be y.

We know that -

Dividend = Quotient Divisor + Remainder

According to question -

3x = 4y + 8

⇒ 3x - 4y = 8.....(1)

and, 5y = 3x + 5

⇒ - 3x + 5y = 5.....(2)

From equation (1), we get -

x = (4y + 8)/3.....(3)

Substituting the value of x in equation (2), we get -

⇒ y - 8 = 5

∴ y = 13

substituting the value of y in equation (3), we get -

x = 20

Thus, the numbers are 20 and 13.