Question

The sum of two numbers is 50. If the larger number is divided by the smaller number we get 1/2. 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.


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