Question

in a two digit number the tens digit is greater than the units digit the product of the digits being 27 and their difference being 6 find the number​

Answer 1

The two digit number is 39 .

Step-by-step explanation:

Let x = tens digit

y= unit digit

The tens digit is greater than the units digit.

i.e. x > y

Product of the digits being 27 .

xy = 27

⇒ $y=\dfrac{27}{x}$         (1)

Their difference being 6.

x-y= 6            (2)

Put value of y from (1) in (2) , we get

$x-\dfrac{27}{x}=6\\\\\Rightarrow\ x^2-27=6x\\\\\Rightarrow\ x^2-6x-27=0\\\\ \Rightarrow\ x^2+3x-9x-27=0\\\\ (x+3)(x-9)=0\\\\ x=-3\ or\ x=9$

x cannot be negative , so x =9

Then,$y= \dfrac{27}{9}=3$

Hence , the two digit number is 39.

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The difference between a two-digit number and the number obtained by interchanging the two digits of the number is 9. The sum of the two digits of the number is 15. What is the product of the two digits of the two digit number?