Question

Sum of two numbers is 13 and their product is 40. Then the greater number exceeds the
smaller number by ?

Answer 1

Answer: 3

Step-by-step explanation:

Let the two numbers be x and y .

So x + y = 13

=> x = 13 - y              (i)

And xy = 40            (ii)

Substituting x in (ii) from (i), we get :-

(13 - y)y = 40

=>  13y - y² = 40

=> y² - 13y + 40 = 0

=> y² - 8y - 5y + 40 = 0

=> (y - 8)(y - 5) = 0

So y = 8 or 5 .

If y = 8 , then x = 5

If y = 5 , then x = 8 .

So the larger number is 8, and the smaller number is 5 .

∴ The larger number exceeds the smaller one by (8 - 5) = 3

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