Question

The sum of the digits of a two-digit number is 12. If the digits are reversed, seven times the new number equals to four times the original number. Find the number.
1. 57
2. 75
3. 84
4. 48

Answer 1

Correct Answer - Option 3 : 84

Given:

The sum of the digits of a two-digit number = 12

Calculation:

Let the two digit number be 10x + y

Sum of digits (x + y) = 12.....(1)

According to the question

⇒ 4(10x + y) = 7(10y + x)

⇒ 40x + 4y = 70y + 7x

⇒ (70y – 4y) = (40x – 7x)

⇒ 66y = 33x

⇒ x/y = 2/1

 Now,

⇒ 2x + x = 12

⇒ 3x = 12

⇒ x = 4

Now,

First number = 2x = (2 × 4) = 8

Second number = x = 4

∴ The required number is 84