Question

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.

Answer 1

We know:

Dividend = Divisor × Quotient + Remainder

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

Then, we have:

3x = y × 4 + 8 or 3x – 4y = 8   ...(i)

5y = x × 3 + 5 or –3x + 5y = 5   ...(ii)

On adding (i) and (ii), we get:

y = (8 + 5)

y = 13

On substituting y = 13 in (i) we get

3x – 4 × 13 = 8

⇒ 3x = (8 + 52)

⇒ 3x = 60

⇒ x = 20

Hence, the larger number is 20 and the smaller number is 13.