Question

A two digit number is such that the product of the digits is 14. When 45 is added to the

number then the digits are reversed. Find the number.​

Answer 1

Answer:

47 I the answer

Step-by-step explanation:

it's help you

Answer 2

Answer :

• The number is 27.

Given :

• A two digit number is such that the product of the digits is 14.
• When 45 is added to the number then the digits are reversed

To find :

• The number

Solution :

• Let the units digits be x
• Let the tens digits be y

Given, A two digit number is such that the product of the digits is 14 then,

• xy = 14

⟹ xy = 14

⟹ y = 14/x

y = 14/x ..... equation (1)

And also Given that , when 45 is added to the number then the digits are reversed so,

• (10y + x) + 45 = 10x + y

⟹ (10y + x) + 45 = 10x + y

⟹ 9y - 9x = -45

⟹ y - x = 5

y - x = 5 ..... equation (2)

Now , from equation (1) and equation (2) we get,

⟹ y = 14/x + y - x = 5

⟹ 14/x - x = -5

⟹ 14 - x² / x = -5

⟹ 14 - x² = - 5

⟹ x² - 5x - 14 = 0

⟹ x² - (7 - 2)x - 14 = 0

⟹ x² - 7x + 2x - 14 = 0

⟹ x(x - 7) + 2(x - 7) = 0

⟹ (x - 7) (x + 2) = 0

⟹ x - 7 = 0 or x + 2 = 0

⟹ x = 7 or x = -2

So , digit cannot be negative.

Now, putting the value of x = 7 in equation (1) we get,

⟹ y = 14/x

⟹ y = 14/7

⟹ y = 2

• y = 2
• x = 7

Now , we have to find the number :

⟹ 10 × y + x

⟹ 10 × 2 + 7

⟹ 20 + 7

⟹ 27

Hence , The number is 27.