Question

the sum of the digits ina two digit number is 7. if the digits are reversed and the new number decreased by 2 equals twice the original number. find the 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 :-

$\longrightarrow \sf x+y = 7 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .........................(1)$

According to the second condition :-

$\longrightarrow \sf 2(10x+y) = 10y+x-2 \\\\\longrightarrow 20x+2y = 10y+x - 2 \\\\\longrightarrow 20x-x+2y-10y = -2 \\\\\longrightarrow 19x-8y = -2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .........................(2)$

Equation (1) × 8 :-

$\longrightarrow\sf 8x+8y = 56 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .........................(3)$

Equation (2) + Equation (3) :-

$\longrightarrow \sf 27x = 54 \\\\\longrightarrow \bf x = 2$

Substitute the value of x in eq (1) :-

$\longrightarrow \sf 2+y = 7 \\\\\longrightarrow \bf y = 5$

Two digit number = 25