Question

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

Answer 1

Answer:

this is the answer I hope you got that question true.

Answer 2

Required answer:-

$\large{ \boxed{ \boxed{ \rm{5 \: or \: 9}}}}$

Step-by-step explanation:

Let us assume that the unit digit be x. Then, the ten's digit will be x - 3 according to first condition given in Q.

Now,

According to 2nd condition, the product of the two digits of the number will be: x(x - 3). And the no. is 10(x - 3) + x.

And when the product of the two digits is subtracted from the number, the result is 15. Which means,

⇒ 10(x - 3) + x - x(x - 3) = 15

⇒ 10x - 30 + x - x² + 3x = 15

⇒ - x² + 10x + 3x + x - 30 - 15 = 0

⇒ - x² + 14x - 45 = 0

⇒ x² - 14x + 45 = 0

Finding the values of x by Middle term factorisation,

⇒ x² - 5x - 9x + 45 = 0

⇒ x(x - 5) - 9(x - 5) = 0

⇒ (x - 9)(x - 5) = 0

From here, we can say that x = 5 or 9

Let x = 5 ⇒ Then, x - 3 = 2

Then the number is 25.

Let x = 9 ⇒ Then, x - 3 = 6

Then the number is 69.

Quick check:

The number is 25. Product of digits = 10

25 - 10 = 15 (Condition satisfied✓)

The next possibility is 69.Product of digits = 54

And, 69 - 54 = 15 (Condition satisfied✓)