Question

If it costs ${\text{Rs}}.10$ a kilometre to fly and ${\text{Rs}}.2$ kilometre to drive. If one travels $200\;{\text{km}}$ covering $x\;{\text{km}}$ of the distance by flying and the rest by driving, then the cost of trip is
A. ${\text{Rs}}.2,000$
B. ${\text{Rs}}.24,000$
C. ${\text{Rs}}.\left( {8x + 400} \right)$
D. ${\text{Rs}}{\text{.}}\left( {12x + 400} \right)$

Answer 1

Hint:
Choose variables to represent unknown, write down the equation for the given problem in terms of assumed unknown and solve the equation to find the value.

Complete step by step solution:
A word problem is a mathematical practice where significant information on the problem is presented in ordinary form rather than in mathematical expression. A word problem is a maths question written as one sentence or more that requires children to apply their maths knowledge to a real-life scenario.
The easiest way to solve the word problem is to represent unknown numbers with variables, translate the rest of the word problem into a mathematical expression and finally solve the problem. Word problem is a technique of thinking how to determine the problem and solve it.
Word problem develops the mental, logical thinking of an individual. It makes him/her different from others in career and life. It improves the solving method of students and makes them extraordinary from others.
Let the distance travelled by flying be $x\;{\text{km}}$ and according to question the distance travelled by flying is $200\;{\text{km}}$.
Therefore,
The distance travelled by driving is $\left( {200 - x} \right)\;{\text{km}}$.
Now, the coast of the trip can be calculated by adding the cost of flying and driving. Thus,
Cost of trip is,
$
  10x + 2\left( {200 - x} \right) \\
   \Rightarrow 10x + 400 - 2x \\
   \Rightarrow 8x + 400 \\
 $

Hence, the option (C) is correct.

Note:
On solving the word problems, always be careful where you need to take the English words and solve them into mathematics. These types of questions are always based on representing the unknown numbers with variables on the given information.