Question
The sum of the digits of a two-digit number is 7. If the digits are reversed, the number is reduced by 27. Find the number?
Hint:
let the number be xy i. e 10x + y = xy where x and y are digits of the number
Given sum of digits = 7 (i. e x + y =7)
If digits are reversed the number is reduced by 27 (i.e xy - yx =27)
The correct answer is: 2 sisters
Ans :- 52 is the number which satisfies the given conditions.
Explanation :-
let the number be xy i.e 10x + y = xy where x and y are digits of the number
Step 1:- Find the equation using sum of digits = 7
Sum of digits = 7
— Eq1
Step 2:- Find the equation using the 2nd condition.
If the digits are reversed, the number is reduced by 27.
xy - yx = 27 
— Eq2
Step 3:- Find x by eliminating y
Adding Eq1 and Eq2
We get 
∴x = 5
Step 4:- Find the value of y by substituting the x =5 in Eq1
∴y = 2
∴ number xy = 52 is the number that satisfies the given condition.
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