Question

Ten children are standing in a line. Each child has some chocolates with him. If the first child attempted to double the number of chocolates with each of the others he would fall short by two chocolates. If the second child took two chocolates from each of the remaining, he would have three chocolates less than what the first child initially had. Find the total number of chocolates with the third to the tenth child.
A) 18
B) 19
C) 23
D) 21

Answer 1

Hint:
Here we need to find the total number of chocolates. For that, we will first assume the number of chocolates with each of the children as any variable. Then we will use the conditions given in the questions to form two equations. After solving these two equations, we will get the required number of chocolate with the third to the tenth child.

Complete step by step solution:
Let the first child have $x$ number of chocolates, the first child has $y$ number of chocolates and the sum of the number of chocolates with the remaining children is $z$.
Since, the first child will try to double up all other chocolates i.e., he will give $y$ number of chocolates to the second and \[z\] number of chocolates to the remaining children.
And the first child will fall short of 2 chocolates.
Now, we will form the equation with the above condition.
$ \Rightarrow x - y - z = - 2$ ………. $\left( 1 \right)$
The second condition is that when the second child took two chocolates from the remaining children, he got 3 chocolates less than the number of chocolates of the first child.
The number of chocolates taken by the second child is equal to $2 \times 9 = 18$.
Therefore, the equation formed will be
$ \Rightarrow x - y - 18 = 3$ ………… $\left( 2 \right)$
Subtracting equation 2 from equation 1, we get
\[\begin{array} \underline \begin{array} x - y - z = - 2\\ - x \mp y \mp 18 = - 3\end{array} \\ - z + 18 = - 5\end{array}\]
Now we got the equation as $ - z + 18 = - 5$.
On adding and subtracting the terms, we get
$ \Rightarrow z = 23$
Therefore, the total number of chocolates with the third to the tenth child is equal to 23.

Hence, the correct option is option C.

Note:
Here, we have formed two linear equations. A linear equation is a type of equation where the highest degree of the variable is 1. A linear equation can have only one solution. Apart from the linear equations, the other types of equations are quadratic equations, cubic equations, and so on. In a quadratic equation, the highest degree is 2 whereas in cubic equations, the highest degree is 3.