Question

The sum of the digits of a 2-digit number is 7. If the digits are reversed , the new number increased by less than 4 times the original number . Find the original number.​

Answer 1

Appropriate Question:

• The sum of the digits of a 2-digit number is 7. If the digits are reversed, the new number increased by 3 less than 4 times the original number. Find the original number.

Given that:

• The sum of the digits of a 2-digit number is 7.

To Find:

• Find the original number.

Let us assume:

• Tens digit be x.
• Ones digit = 7 - x
• Original number = 10x + (7 - x)

The digits are reversed.

• New number = 10(7 - x) + x

The new number increased by 3 less than 4 times the original number.

New number = 4{Original number} - 3

↠ 10(7 - x) + x = 4{10x + (7 - x)} - 3

↠ 70 - 10x + x = 4{10x + 7 - x} - 3

↠ 70 - 9x = 40x + 28 - 4x - 3

↠ 70 - 28 + 3 = 40x - 4x + 9x

↠ 45 = 45x

↠ 45/45 = x

↠ 1 = x

↠ x = 1

Original number:

↠ 10x + (7 - x) = 10(1) + (7 - 1)

↠ 10x + (7 - x) = 10 + 6

↠ 10x + (7 - x) = 16

Hence,

• The original number is 16.