Question

the taxi charges of city is fixed together with the charge for distance covered for 10 km.he paid 75 and for 15 km he paid 110 ? what are fixed charges and charges per km.

Answer 1

Basic Concept Used :-

Writing System of Linear Equations from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

Solution:-

• Let fixed charges be Rs x

and

• Let charge per km be Rs y.

According to statement,

For a distance of 10 km, charge is Rs 75.

$\bf\implies \:x + 10y = 75 - - - (1)$

According to statement,

For a distance of 15 km, charge is Rs 110.

$\bf\implies \:x + 15y = 110 - - - (2)$

On Subtracting, equation (1) from equation (2), we get

$\rm :\longmapsto\:x + 15y - (x + 10y) = 110 - 75$

$\rm :\longmapsto\:x + 15y - x - 10y = 35$

$\rm :\longmapsto\:5y = 35$

$\bf\implies \:y = 7$

On substituting the value of y = 7, in equation (1), we get

$\rm :\longmapsto\:x + 10 \times 7 = 75$

$\rm :\longmapsto\:x + 70 = 75$

$\bf\implies \:x = 5$

Hence,

• Fixed charge = Rs 5

• Charge per km = Rs 5