Question

A 2-digit number is 3 times the sum of its digits. If 45 is added to the number, its digits are interchanged. The sum of digits of the number is

Answer 1

Answer:

Number = 27

sum of digits = 9

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Step-by-step explanation:

let say number = 10x + y

10x + y = 3 (x+y)

7x = 2y

10y+x = 10x + y + 45

9y -9x = 45

y -x = 5

2y - 2x = 10

7x - 2x = 10

5x = 10

x = 2

7*2 = 2y

y = 7

number = 27

Answer 2

Answer is 27

Let the tens digit of the number is X
unit. digit of the number is Y

so the number is X×10 +Y = 10X+Y

sum of digits = X+Y

According to Question

10X+Y= 3(X+Y)

7X-2Y=0................................1


&
10X+Y +45 = Y×10 +X

10X+Y+45 =10Y+X

9X-9Y=-45
X-Y=-5........................................2

7X-2Y=0 ×1
X-Y =-5 ×2

7X-2Y=0
2X-2Y=-10


subtracting equation 2 from 1
___________________________


5X=10
X=2
&
Y=2+5=7

_______________

So the sum of Number is (X+Y) =2+7=9

Verification


1st Case

Number =27
Sum =2+7=9
9×3=27 ..... verified

2nd Case

27+45= 72 verified