Question

The railway fare from Delhi to Meerut for 3 adults and 2 children is ₹ 250 and for 2 adults and 3 children is ₹ 225. Find the fare for one adult and for one child.

Answer 1

Given:

• The railway fare from Delhi to Meerut for 3 adults and 2 children is ₹ 250.
• The fare for 2 adults and 3 children is ₹ 225.

Let’s denote:

Fare of one adult = ₹ x

Fare of one child = ₹ y

Step-wise calculation:

Step 1: Form equations based on the given information:

For 3 adults and 2 children: 3x + 2y = 250

For 2 adults and 3 children: 2x + 3y = 225

Step 2: Solve the system of linear equations:

From the first equation: 3x + 2y = 250   ...(i)

From the second equation: 2x + 3y = 225   ...(ii)

Multiply (i) by 3: 9x + 6y = 750   ...(iii)

Multiply (ii) by 2: 4x + 6y = 450   ...(iv)

Step 3: Subtract equation (iv) from (iii):

(9x + 6y) – (4x + 6y) = 750 – 450

9x – 4x = 300

5x = 300

x = `300/5`

x = 60

Step 4: Substitute x = 60 into equation (i):

3(60) + 2y = 250

180 + 2y = 250

2y = 250 – 180

2y = 70 

y = `70/2`

y = 35

Fare for one adult = ₹ 60.

Fare for one child = ₹ 35.