Q. 7

# The difference between two numbers is 5 and the difference between their squares is 65. Find the numbers.

Let us assume the two numbers be x and y, where x > y

So, according to question we have:

x – y = 5 …(i)

x2 – y2 = 65 …(ii)

Now, by dividing (ii) by (i) we get:

x + y = 13 …(iii)

Now, adding (i) and (ii) we get:

2x = 18

Putting the value of x in (iii), we get:

9 + y = 13

y = 13 – 9

y = 4

The two numbers are 9 and 4

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