Question

The sum of the digits of a two-digit number is 14. The number formed by reversing the digits is 36 less than the original number. Find the original number.
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Answer 1

Answer:-

Let the number be (10x + y).

Given:

Sum of the digits = 14

→ x + y = 14

→ x = 14 - y -- equation (1).

And,

The number formed by reversing the digits 36 less than the original number.

→ 10x + y - 36 = 10y + x

Substitute x value from equation (1).

→ 10(14 - y) + y - 36 = 10y + 14 - y

→ 140 - 10y + y - 36 = 9y + 14

→ - 9y - 9y = 14 + 36 - 140

→ - 18y = - 90

→ y = - 90/ - 18

→ y = 5

Substitute y value in equation (1)

→ x = 14 - y

→ x = 14 - 5

→ x = 9

The number = 10(9) + 5 = 95.

Hence, the number is 95.

Answer 2

✬ Original Number = 95 ✬

Step-by-step explanation:

Given:

• Sum of the digits of a two digit number is 14.
• Number formed by reversing digits is 36 less than original number.

To Find:

• What is the original number ?

Solution: Let the unit and tens digit of number be y and x respectively. Therefore,

➟ x + y = 14 or

➟ x = (14 – y)........(1)

So original number will be :-

➯ Original number = (10x + y)

After reversing digits the number formed is:-

➯ Reversed number = (10y + x)

A/q

• Reversed number is 36 less than original number.

$\implies{\rm }$ (10x + y) = (10y + x) + 36

$\implies{\rm }$ 10x – x = 10y – y + 36

$\implies{\rm }$ 9x = 9y + 36

$\implies{\rm }$ 9(14 – y) = 9y + 36

$\implies{\rm }$ 126 – 9y = 9y + 36

$\implies{\rm }$ 126 – 36 = 9y + 9y

$\implies{\rm }$ 90 = 18y

$\implies{\rm }$ 90/18 = y

$\implies{\rm }$ 5 = y

So,

➭ Unit digit of number is y = 5

➭ Tens digit = x = (14–y) = 14–5 = 9

Hence, The original number is

➫ (10x + y)

➫ 10(9) + 5 = 95