Question

In two-digit number, first digit is four times of second digit. Adding this to
the new number formed by reversing the digits, 110 is obtained. Find the
numbers.​

Answer 1

Answer:

Let the tens digit be X and unit digit be 4x

original number be 10(X)+4x=14x

Also 14x+41x=110

55x=110

X=110/55

X=2

therefore original number is 28

Answer 2

Answer:

Let the one’s digit be x.

∴ Ten’s digit is 4x.

∴ Number = 10 x Ten’s digit + One’s digit

= 10 x (4x) + x

= 40x + x

= 41x

Now the digits are reversed, one’s digit = 4x, and ten’s digit = x

∴ Number = 10 x ten’s digit + one’s digit

= 10 x x + 4x

= 10x + 4x

= 14x

According to question

41x + 14x = 110

⇒ 55x = 110

x = $\frac{110}{55}$

⇒ x = 2

Hence, One’s digit = 2

and Ten’s digit =4 x 2 = 8

Number = 82

Again, if one’s digit is 4 times of ten’s digit, then number = 28

Hence, the required number is 82 or 28.