Answer :

Let the first number be *x* and the second number is 27 − *x*.

[As the sum of both the numbers is 27]

Therefore, their product = *x* (27 − *x*)

It is given that the product of these numbers is 182.

x (27 – x) = 182

- x^{2} + 27x - 182 = 0

Changing the signs on both sides we get,

x^{2} - 27x + 182 = 0

Factorizing we get , 13 and 14 are the numbers whose sum is 27 and product is 182

x^{2} – 13x – 14x + 182 = 0

= x(x – 13) – 14 (x – 13)= 0

= (x – 13) (x – 14) = 0

Either x – 13 = 0 or *x* − 14 = 0

i.e., *x* = 13 or *x* = 14

If first number = 13, then

Other number = 27 − 13 = 14

If first number = 14, then

Other number = 27 − 14 = 13

**Therefore, the numbers are 13 and 14.**

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