NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.2 Question 3(iv)

NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.2 Question 3(iv)

Question:

Form the pair of linear equations for the following problems and find their solution by substitution method.

The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?

Given:

For a distance of 10 km, the charge paid is Rs 105. For a journey of 15 km, the charge paid is Rs 155.

To Find:

The fixed charges and the charge per km. Also, the charge for travelling a distance of 25 km.

Formula:

Let the fixed charge be Rs x and the charge per km be Rs y. Then the equations are:

x + 10y = 105

x + 15y = 155

Solution:

From the first equation, x = 105 - 10y

Substitute this value of x in the second equation:

105 - 10y + 15y = 155

⇒ 5y = 155 - 105

⇒ 5y = 50

⇒ y = 50 5 = 10

Substitute y = 10 in x = 105 - 10y

⇒ x = 105 - 10(10) = 105 - 100 = 5

Therefore, fixed charge (x) = Rs 5 and charge per km (y) = Rs 10

Charge for 25 km = 5 + 25(10) = 5 + 250 = Rs 255

Result:

Fixed charges = Rs 5

Charge per km = Rs 10

Charge for 25 km = Rs 255

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