Question

the tens digit of a two digit number is less by 3 than the unit digit. If the product of the two digits are subtracted from the number, the result is 15. Let us write the unit digit of the number by calculation​

Answer 1

                    SOLUTION

Let us Assume that the digit in the units place is x

∵  tens digit is less by 3 than the unit digit.

Digit in tens place will be = 10(x - 3)

So, our two digit number will be ,

10(x - 3) + x

$\implies$ 10x - 30 + x  =  11x - 30

In the question it is said that :- If the product of the two digits are subtracted from the number, the result is 15

(11 x - 30 ) - x(x-3) = 15

$\implies$ 11x - 30 - x² - 3x = 15

$\implies$ - x² + 14x - 45 = 0 $\longrightarrow$ (1)

Multiplying (1) by -1 in order to make x² positive

$\implies$  x² - 14x + 45 = 0

Now Let us Solve x² - 14x + 45 = 0 , to find the value of x .

If we split the middle term ,

Product = 45

   and

Sum = -14

$\implies$ x² - 5x - 9x + 45 = 0

$\implies$ x(x-5) - 9(x-5) = 0

$\implies$ (x-5)(x-9)

∴ x = 5

    and

   x = 9

Therefore the unit place can take values of  5 and 9