Question

5. The sum of the digits of a 2-digit number is 7. If
the number formed by reversing the digits is
more than the original number by 27. Find the
original number.​

Answer 1

Answer:

25

Step-by-step explanation:

Let x and y be the digits at tens and ones place respectively.

Let A be the number formed by these digits.

Therefore, A=10x+y……….(1)

According to the question.

x+y=7…………(2)

Let B be the new number formed by reversing the digits.

Therefore, B=10y+x……….(3)

According to the question.

B=27+A

=>(10y+x)=27+(10x+y)

=>(10y+x)-(10x+y)=27

=>9y-9x=27

=>9(y-x)=27

=>y-x=27/9=3…………..(4)

Adding equations (2) and (4).

(x+y)+(y-x)=7+3=10

=>2y=10

=>y=5 and x=7–5=2……….from equation(2)

Hence,the number is A=10x+y=10*2+5=25