Maths-
General
Easy

Question

A number which is formed by two digits is 3 times the sum of the digits. While interchanging the digits it is 45 more than the actual number. Find the number.

Hint:

let the number be xy i. e 10x + y = xy where x and y are digits of the number
Given The number formed is 3 times the sum of digits   (i. e 10x+y =3(x + y))
If digits are reversed the number is increased by 45 (i. e xy +45 = yx)

The correct answer is: 27


    Ans :- 27 is the number which satisfies the given condition.
    Explanation :-
    Step 1:- frame the equations from the given set of conditions .
    Given The number formed is 3 times the sum of digits
    10 x plus y equals 3 left parenthesis x plus y right parenthesis not stretchy rightwards double arrow 7 x equals 2 y not stretchy rightwards double arrow y equals 7 over 2 x— Eq1
    If digits are reversed the number is reduced by 45
    y x minus x y equals left parenthesis 10 y plus x right parenthesis minus left parenthesis 10 x plus y right parenthesis equals 45
    not stretchy rightwards double arrow 9 y minus 9 x equals 45
    not stretchy rightwards double arrow y minus x equals 5—- Eq2
    Step 2:- Substitute Eq1 in Eq2
    We get not stretchy rightwards double arrow 7 over 2 x minus x equals 5
    not stretchy rightwards double arrow 5 over 2 x equals 5
    ∴ x = 2
    Step 3:- find the value of y by substituting x=2 in Eq2
    y minus x equals 5 not stretchy rightwards double arrow y minus 2 equals 5 not stretchy rightwards double arrow y equals 7
    ∴ y = 7
    ∴ 27 is the number which satisfy the given conditions.

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