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

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.

Let us consider, larger number = x and

Smaller number = y

As per the statement,

3x = 4y + 8 …….(1)

5y = 3x + 5 …(2)

Using Substitution method:

Substitute the value of 3x in (2), we get

5y = 4y + 8 + 5

5y – 4y = 13

or y = 13

From (1): 3x = 4 x 13 + 8 = 60

x = 20

Answer:

Larger number = 20

Smaller number = 13

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.