Question

the sum of the digits of a two-digit number is 12. of the digits are reversed. The new number is 4/7 times the original number. Determine the original number

Answer 1

Hello here is your answer by Sujeet yaduvanshi ☝☝☝☝☝☝☝☝☝☝☝☝☝



Let to be 10' unit digit Number x

Let to be 1'unit digit Number y

then,

According to question...


X+y=12 ( I Equation)


Original Number =10y+x

Required Number=10x+y

Again,

10x+y=4/7(10y+x)

7(10x+y)=40y+4x

70x+7y=40y+4x

70x-4x+7y-40y=0

66x-33y=0

33(2x-y)=0

2x+y=0/33

2x+y=0. (Second Equation)



Solving the equation (I) and (ii)


By elimination method:-

x+y=12 *2

2x+y=0*1

2x+2y=24
2x+y=0

___________
y=24


Then,


Putting the value of y in equation (I)



x+y=12

x+24=12
x=12-24

x=-12


Then,

Original Number=10y+x
10*24+(-12)
240-12

228


That's all by """Alone Boy''''. (Sujeet yaduvanshi)