Question

The sum of two numbers is 80. The larger number exceeds four times the smaller one by 5. Find the numbers.

Answer 1

Let the larger number be x and the smaller number be y.

Then as per the question

x + y = 80   ...(i)

x = 4y + 5

x – 4y = 5   ...(ii)

Subtracting (ii) from (i), we get

5y = 75

`y = 75/5`

⇒ y = 15

Now, putting y = 15 in (i), we have

x + 15 = 80

x = 80 – 15

⇒ x = 65

Hence, the numbers are 65 and 15.