Math, asked by shraavni78, 2 months ago

A number consists of two digits whose sum is 8 if 18 is added to the number its digit are reversed. Find the number​

Answers

Answered by Yuseong
5

Given :

• A number consists of two digits whose sum is 8.

• If 18 is added to the number its digit are reversed.

To calculate :

• The original number.

Calculation :

Let the original number be 10a + b.

According to the question :

\sf{ \implies a + b = 8 }

[ Since, the sum of the two digits of a number is 8.]

So,

\sf{ \implies a + b = 8 }

\sf{ \implies  b = 8 - a } . . . . . . . . ( Eq. 1 )

Also, according to the question:

\sf{ \implies 10a + b + 18 = 10b + a } . . . . . . . . . (Eq. 2)

[Since, if 18 is added to the number its digit are reversed.]

Now, substitute the value of b from equation 1 in equation 2 in order to find the value of a .

Calculating the value of 'a' :

\sf{ \implies 10a + (8-a) + 18 = 10(8-a) + a }

\sf{ \implies 10a + 8-a + 18 = 80 - 10a + a }

\sf{ \implies 9a + 8 + 18 = 80 - 9a }

\sf{ \implies 9a + 26 = 80 - 9a }

\sf{ \implies 9a + 9a = 80 - 26 }

\sf{ \implies 18a = 54 }

\sf{ \implies a = \dfrac{54}{18} }

 \implies  \boxed {\sf \red{a = 3 }}

Calculating the value of 'b' :

Now, substitute the value of a in the equation 1 to find the value of b.

\sf{ \implies  b = 8 - a }

\sf{ \implies  b = 8 - 3 }

 \implies  \boxed {\sf \red{b = 5}}

Now, the original number :

\sf{ \implies  Original \: number = 10a + b }

\sf{ \implies  Original \: number = 10(3) + 5 }

\sf{ \implies  Original \: number = 30 + 5 }

 \implies \boxed{\sf\green{  Original \: number = 35 }}

Therefore, the number is 35.

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