Question

The sum of the digits of a two-digit number is 7. If the number formed by reversing the
digits is less than the original number by 27, find the original number.​

Answer 1

Answer:

52

Step-by-step explanation:

let the number be 10x+y

sum of digits=7

X+Y=7 (equation 1)

number obtained by reversing the digits= 10y+X

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

10x + y -10y -x=27

9x – 9y=27

9(x-y)=27

x-y=27/9=3 (equation 2)

by adding both equations:

X+Y=7

X-Y=3

2X=10

X=5

if X=5 then y = 7-5

Y=2

answer =10x+y=50+2=52

Answer 2

Answer....

________________________________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

________________________________Answer can be 25 and 52... depending upon the you, how you have taken the value of x and y..

________________________________ hope it helps you... ☺️✌