Question

For a journey the cost of a child ticket is $\dfrac{1}{3}$of the cost of an adult ticket. If the cost of the ticket for 4 adults and 5 children is Rs.85, the cost of child ticket is
A. Rs.15
B. Rs.6
C. Rs.10
D. Rs.5

Answer 1

Hint:First, assume the original price of the ticket of an adult to be any variable(x). Now the cost of tickets for children are added given that the cost of a child is $\dfrac{1}{3}$ of an adult. This total amount is to be equated with Rs.85.

Complete step-by-step answer:
We are given that the tickets were purchased of Rs.85. Moreover, the cost of a child ticket is $\dfrac{1}{3}$of the cost of an adult ticket.
We have to find the price of a child's ticket.
Let the price of the ticket of an adult be x.
Since, there are a total of 4 adults the cost of tickets of all the adults is 4x.
Now, the cost of a child’s ticket is $\dfrac{1}{3}$of the cost of an adult ticket. This can be mathematically shown as$\dfrac{1}{3}x$.
Since, there are a total of 5 children the cost of tickets of all the children is$\dfrac{5}{3}x$.
Now, the total money for which tickets have been bought is Rs.85 which is in addition to the total cost of children and adults.
Mathematically it can be written as,
$\begin{gathered}
   \Rightarrow \dfrac{5}{3}x + 4x = 85 \\
   \Rightarrow \dfrac{{5x + 12x}}{3} = 85 \\
   \Rightarrow \dfrac{{17x}}{3} = 85 \\
   \Rightarrow x = \dfrac{{85 \times 3}}{{17}} = 15 \\
\end{gathered} $
Therefore, 15 is the cost of an adult ticket. And because the cost of a child's ticket is $\dfrac{1}{3}$ of the cost of an adult ticket. The cost of a child's ticket is 5.
Therefore, option (D) 5 is the correct option.

Note:While assuming a variable it is necessary to specify which quantity is assumed. If not defined chances of error are there. Linear equations in one variable will have a single variable. Linear equations in two variables will have 2 different variables.