Question

Please help me with this one

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Answer 1

62

Explanation:

The sum of two digits in a number is 8. Let the left digit represent x and the right y.

x + y = 8 if the digits change order, the new number is 36 less than the old number.

Since 26 + 36 = 62 Therefore, x=2 and y=6 The number is 62.

Answer 2

Original number = 10x + y - such considered as it is a two digit number.

The sum of digits is:

⇒ x + y = 8

⇒ y = 8 -x ← Equation 1

The interchange number: 10y + x

If they interchange, the number is 36 less than original number.

⇒ 10y + x = (10x + y) - 36 (add/subtract integers)

⇒ 10y - y = 10x - x - 36 (simplify)

⇒ 9y = 9x - 36 (divide both sides by 9)

⇒ y = x - 4 ← Equation 2

Substitute Both the equations:

⇒ x - 4 = 8 - x ⇒ 2x = 12 ⇒ x = 6

Then find y : x - 4 = 6 - 4 = 2

• Original Number: 10x + y = 10(6) + 2 = 62

• The Interchange number: 10y + x = 10(2) + 6 = 26

Original Number is 62