Question

The digit in the tens place of a 2-digit number is four times the digit in the ones place. If the digits are reversed, the new number is 27 less than the original number. Find the original number and check the solution.​

Answer 1

$\large\underline{\sf{Solution-}}$

Let digit in ones place be x.

So,

Digit in tens place be 4x.

Thus

Original Number = 10 × 4x + x × 1 = 40x + x = 41x

Reverse number = 10 × x + 4x × 1 = 10x + 4x = 14x

According to given condition,

The reverse number is 27 less than the original number.

$\rm :\longmapsto\:41x - 14x = 27$

$\rm :\longmapsto\:27x = 27$

$\bf\implies \:x = 1$

Thus,

2 digit number = 41x = 41 × 1 = 41.

Verification :-

Two digit number = 41

Reverse number = 14

So,

Original number - Reverse number = 41 - 14 = 27.

Hence, verified.