Question

one digit of the two digit number is 4 times the other digit the number obtained by increasing the digit is greater than the original number by 54.find the original number ​

Answer 1

Solution :-

Let :-

Digit in ten's place = x

Digit in one's place = y

Two digit number = 10x + y

According to the first condition :-

$\longrightarrow \sf y=4x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ......................(1)$

According to the second condition :-

$\longrightarrow \sf 10x+y+54 = 10y+x\\\\\longrightarrow 10x-x+y-10y = -54 \\\\\longrightarrow 9x-9y - 54 \\\\\longrightarrow x-y = -6 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ......................(2)$

Substitute the value of y in eq (2) :-

$\longrightarrow \sf x-4x = -54 \\\\\longrightarrow -3x = -6 \\\\\longrightarrow \bf x = 2$

Substitute x = 2 in eq (1) :-

$\longrightarrow \sf y = 4 \times 2 \\\\\longrightarrow \bf y = 8$

Two digit number = 28