Math, asked by alcuinsangeerthana4, 2 months ago

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​

Answers

Answered by selviparthibann
1
Check the screenshot for explanation
Attachments:
Answered by ImperialGladiator
10

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

Similar questions