Question

There were 252 chocolates to be divided into three groups A , B and C. A certain number of chocolates were selected from group A and distributed to groups B and C such that the number of chocolates in each of these groups was doubled.

Then, some chocolates were removed from Group B and distributed to groups A and C, such the the number of chocolates in each of these two groups was also doubled. After that, selection and distribution of chocolates continued from Group C to Group A and B.

At the end, the number of chocolates in group B was twice of A while the number of chocolates in group A was twice of C. Find the number of chocolates in the largest group of chocolates at first.

Answer 1

Heyy bro !
Here is your answer
Final Result : 135
A = 135 B = 81 C = 36

Initially,
Let the no. of chocolates of A, B and C be x,y and z respectively.
Then,
x+y+z = 252 (given) ------(1)

Now,
1) A certain no. of chocolates is selected from group A and distributed to groups B and C in such a way that no. of chocolates in Group B and C is doubled.

This is possible when
B has 2y and C has 2z chocolates
i.e., We took z and y chocolates from A.

Remaining no. of chocolates in A
= x - (y+z)
= x-y-z
At this stage ,
No. of chocolates in Group:
A. = x-y-z
B = 2y
C. = 2z

2) Now, same procedure took place in Group B:

Here,
No. of Chocolates doubled in C and A .
i.e.,
A = 2(x-y-z) = 2x-2y-2z

C = 2(2z) = 4z
Similarly as done in A in (1).
In B
= 2y - [2z + (x -y-z)]
= 3y-x-z

At this stage , No. of chocolates in Group:
A = 2x-2y-2z
B =3y-x-z
C = 4z

3) Now, same procedure took place in Group C:

Here,
No. of Chocolates doubled in B and A .
i.e.,
A = 2(2x-2y-2z)
B = 2(3y-x-z)

Similarly as done in A in (1).
In C
= 4z - [(3y-x-z)+(2(x-y-z)]
= 7z-y-x

At this stage , No. of chocolates in Group:
A = 2(2x-2y-2z)
B =2(3y-x-z)
C = 7z-y-x

Now, Finally
According to the question, we get
B = 2 A
=> 2(3y-x-z) = 2 * 2(2x-2y-2z)

=> -5x+7y +3z = 0---(2)


And A = 2C
On substituting values ,
=> -3x + y + 9z =0 -----(3)



On solving eq. (1) , (2) & (3),

we get
x = 135
y = 81
z = 36


Hope you understand my answer and it may help you.