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

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