Question: The sum of two numbers is 60 and their difference is 10. Find the numbers.

Solution:

Let, one of the two numbers be 'x' and the other number be 'y'. 

Since, the difference is not zero, the numbers are not equal. Let, x be there greater number.

According to the question,

Condition I,

Sum of two numbers is 60, or, x +y= 60
or, x = 60-y - (i)

Condition II,

Difference of two numbers is 10, or, x-y=10
or, x = 10+y - (ii)

Now,
Adding equations (i) and (ii), we get,

or, x +x = 60-y +10+y
or, 2x = 70
or, x = \frac{70}{2}
\therefore x = 35

Put value of x in equation (i), we get,
or, 35 = 60 - y
or, y = 60-35
\therefore y = 25

So, (x,y) = (35,25)

Hence, the required two numbers are 35 and 25.

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