Maths-
General
Easy

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
    x plus y equals 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 not stretchy rightwards double arrow left parenthesis 10 x plus y right parenthesis minus left parenthesis 10 y plus x right parenthesis equals 27
    not stretchy rightwards double arrow 9 x minus 9 y equals 27 not stretchy rightwards double arrow 9 left parenthesis x minus y right parenthesis equals 27
    not stretchy rightwards double arrow x minus y equals 3 — Eq2
    Step 3:- Find x by eliminating y
    Adding Eq1 and Eq2
    We get x plus y plus x minus y equals 7 plus 3
    not stretchy rightwards double arrow 2 x equals 10
    ∴x = 5
    Step 4:- Find the value of y by substituting the x =5 in Eq1
    not stretchy rightwards double arrow x plus y equals 7 not stretchy rightwards double arrow 5 plus y equals 7
    ∴y = 2
    ∴ number xy = 52 is the number that satisfies the given condition.

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