Question

The sum of a two-digit number and the number formed by interchanging its digits, is 132. If 15 is subtracted from the first number, then the new number is 6 more than 3 times the sum of the digits of the first number. Then, the original number is.​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

Let unit's digit =y and the ten's digit =x 

So, the original number =10x+y 

After interchanging the digits, New number =x+10y 

The sum of the number =10x+y 

The sum of the digit =x+y 

According to the question, (10x+y)+(x+10y)=132

⇒11x+11y=132

⇒11(x+y)=132

⇒x+y=12…(i)

and 10x+y+12=5(x+y)

⇒10x+y+12=5x+5y

⇒10x−5x+y−5y=−12

⇒5x−4y=−12…(ii)

From Eq. (i), we get x=12−y…( iii )

On substituting the value of x=12−y in Eq. (ii), we get 

5(12−y)−4y=−12

⇒60−5y−4y=−12

⇒−9y=−12−60

⇒−9y=−72

⇒y=8

On putting the value of y=8 in Eq. (iii), we get 

x=12−8=4

So, the Original number =10x+y 

=10×4+<

Step-by-step explanation:

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