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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