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) = 13 

On substituting y = 13 in (i) we get 

3x - 4 × 13 = 8 

⇒ 3x = (8 + 52) = 60 

⇒ x = 20 

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