Question

Photo of the answer.The sum of the digits of a 2-digit number is 7. If the digit are reversed,the new number increased by 3 equals 4 times the original number.Find the original number​

Answer 1

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Answer 2

Given :-

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

To find :-

• Original number

Solution :-

Let the tens digit be x then ones digit be y

Original number = 10x + y

• According to the first condition

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

→ x + y = 7 ---(i)

• According to the second condition

If the digit are reversed,the new number increased by 3 equals 4 times the original number.

• Reversed number = 10y + x

→ 10y + x + 3 = 4(10x + y)

→ 10y + x + 3 = 40x + 4y

→ 40x - x + 4y - 10y = 3

→ 39x - 6y = 3

→ 3(13x - 2y) = 3

→ 13x - 2y = 1 ---(ii)

Multiply (i) by 2 and (ii) by 1

• 2x + 2y = 14
• 13x - 2y = 1

Add both the equations

→ 2x + 2y + 13x - 2y = 14 + 1

→ 15x = 15

→ x = 15/15

→ x = 1

Put the value of x in equation (i)

→ x + y = 7

→ 1 + y = 7

→ y = 7 - 1

→ y = 6

Hence,

• Ones digit = y = 6

• Tens digit = x = 1

Therefore,

• Original number = 10x + y = 16

• Reversed number = 10y + x = 61