Question

2. Two numbers are such that when the larger number is divided by the smaller number, both the quotient and the remainder are equal to 2. If five times the smaller number is divided by the larger number, both the quotient and the remainder are also equal to 2. Find the two numbers.​

Answer 1

Let's assume that the smaller number is x and the larger number is y.

From the problem, we can write:

y = 2x + 2 (since the quotient and remainder when y is divided by x are both equal to 2)

5x = 2(y - 2) (since the quotient and remainder when 5x is divided by y are both equal to 2)

Substituting the first equation into the second equation, we get:

5x = 2((2x + 2) - 2)

5x = 4x + 4

x = 4

Substituting x = 4 into the first equation, we get:

y = 2x + 2 = 10

Therefore, the two numbers are 4 and 10