Question

Two bags together contains 50 chocolates. From the first bag, 12 chocolates were given to a child. Then 8 chocolates were taken from the first bag and put into the second bag to make the number of chocolates equal in both bags. How many chocolates were there in each bag.

Answer 1

Hint: To solve this question we will first take the number of chocolates in the 1st bag as x and the number of chocolate in 2nd bag as y. now we know that the total chocolates are 50. Hence we get the first equation in x and y. then 8 chocolates are removed from 1st bag hence the number of remaining chocolates in 1st bag is
x – 8. Now, these 8 chocolates are transferred to 2nd bag hence we get the number of chocolates in 2nd bag is y + 8.
Now the number of chocolates in each bag after this process is the same hence we get our 2nd equation in x and y. hence we can easily find the value of x and y by these two equations

Complete step by step answer:
Now let us call the first bag as A and the second bag is B.
Now let us say bag A has x chocolates and bag B has y chocolates.
Now it is given that number of chocolates in both bags is 50
Hence we get $x+y=50...............(1)$
Now then 8 chocolates are removed from bag A hence the number of remaining chocolates in bag A is x – 8 and these 8 chocolates are transferred to bag B hence we get the number of chocolates in bag B is y + 8.
Now after this transfer we are given that the number of chocolates in both bags are equal.
Hence we have $x-8=y+8$
Now taking y to LHS and – 8 to RHS we get
$x-y=8+8$
Hence $x-y=16...............(2)$
Now adding equation (1) and equation (2) we get
\[\begin{align}
  & x+y+x-y=50+16 \\
 & \Rightarrow 2x=66 \\
 & \Rightarrow x=\dfrac{66}{2} \\
 & \Rightarrow x=33 \\
\end{align}\]
Now substituting the value x = 33 in equation (1) we get
$\begin{align}
  & 33+y=50 \\
 & \Rightarrow y=50-33 \\
 & \Rightarrow y=17 \\
\end{align}$
Hence the 1st bag had originally 33 chocolates and the 2nd bag had originally 17 chocolates.

Note:
Note that while taking the terms from LHS to RHS or from RHS to LHS the sign of the term changes.