Question

In a 2 digit if it is known that it's units digit exceeds its tens digit by 3 and that the product of the given number and the sum of its digit is equal to 175
then the no . Is?​

Answer 1

Answer:

25

Step-by-step explanation:

Let the tens digit be x the units digit is x+3$Therefore, \ the \ number \ is \ 10x + (x+3)*1 = 10x + x +3=11x+3\\Product = 175\\number * sum \ of \ digits = 175\\(11x + 3)(x + (x+ 3)) = 175\\(11x + 3)(2x + 3) = 175\\22x^{2} + 33x + 6x + 9 = 175\\22x^{2} + 39x + 9 = 175\\22x^{2} + 39x - 166 = 0\\x = \frac{-b \± \sqrt{b^{2} - 4ac}}{2a} = \frac{-39 \± \sqrt{39^{2} + 4*22*166}}{2*22}\\\\=\frac{-39 \± \sqrt{1521 + 14608}}{44} = \frac{-39 \± \sqrt{16129}}{44}\\\\=\frac{-39 \± 127}{44}$

$Therefore,\\x = \frac{-39 + 127}{44} \ or \ x = \frac{-39 - 127}{44}\\x = \frac{88}{44} \ or \ x = \frac{-166}{44}\\x = 2 \ or \ x = \frac{-166}{44}\\Now \ we \ reject \ second \ result \ as \ digits \ of \ a \ number \ cannot \ be \ negative\\So, x = 2\\Then \ number \ is \ 11x + 3 = 11*2 + 3 = 22 + 3 = 25$

Therefore

the number is 25