Question

The sum of the digits of a 2-digit number is 7.If the digits are reversed,the number formed is 9 less than the original number.Find the number​

Answer 1

Check the screenshot for explanation

Answer 2

Answer:

The number is 43

Step-by-step explanation:

Let's assume the numbers :

• One's digit $x$
• Ten's digit $y$

Given,

$\to x + y = 7 \bf . . . . . . (i)$

Express the number :

$\to 10x + y$

Reverse the digits :

$\to 10y + x$

${\underline{\boldsymbol{According \: to \: the \: question :}}}$

Given that, $10y + x$ is less than $10x + y$ by 9.

Solving for $\boldsymbol x$ :

$\implies (10x + y) - (10y + x) = 9$

$\implies 10x + y - 10y - x = 9$

$\implies 9x - 9y = 9$

$\implies 9(x - y) = 9$

$\implies x - y = 1 \bf . . . . .(ii)$

Solving equation (i) and (ii) :

$x + y = 7 \\x - y =1 \\{ \underline{ \tiny{( - ) \: \: \: \: \: \: \: \: \: ( + )\: \: \: \: \: \: \: \: \: \: \: \: ( - ) \: \: \: \: \: \: \: \: \: \: }}} \\\implies 2y = 6 \\ \implies y = \frac{6}{2} \\ \implies \: y = 3$

Substitute the value of $\boldsymbol y$ in equation (i) :

$\implies x + y = 7 \\ \implies x + 3 = 7 \\ \implies x = 7 - 3 \\ \implies x = 4 \: \: \: \: \: \: \: \:$

Hence, the number is :

$\to \boldsymbol{10x + y} \\ \sf \to 10(4) + 3 \\ \sf \to 40 + 3 \\ \to \sf \: 43$