Answered

b) In a two-digit natural number, the ten's place digit is 6 less than the unit place digits. If
the product of the digits is 27, find the number.



Answer :

Answer:

  • 39

Explanation:

Let's assume the ten's place digit is 'x' and the unit's place digit is 'y'.

According to the problem, the ten's place digit is 6 less than the unit's place digit, so we can write the equation as:x = y - 6 ---(1)

The product of the digits is 27, so we can write the equation as:

  • x * y = 27 ---(2)

Now, substitute the value of x from equation (1) into equation (2):

  • (y - 6) * y = 27

Expanding the equation:

  • y^2 - 6y = 27

Rearranging the equation:

  • y^2 - 6y - 27 = 0

Now, let's solve this quadratic equation by factoring or using the quadratic formula.

Factoring the equation:

  • (y - 9)(y + 3) = 0

Setting each factor to zero:

  • y - 9 = 0 or y + 3 = 0

Solving for y:

y = 9 or y = -3

Since we are looking for a two-digit natural number, we discard the negative value.

  • So, y = 9.

Now, substitute the value of y into equation (1) to find x:

  • x = y - 6
  • x = 9 - 6
  • x = 3

Therefore, the number is 39.

So, the two-digit natural number is 39.

- Q.E. :))

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