## Case Study Questions for Class 9 Maths Chapter 4 Linear Equations in Two Variables

**Case Study Questions**

**Question 1:**

Anil went to buy some vegetables, he bought ‘x’ kgs. of tomato and ‘y’ kgs. of potato. The total cost of vegetables comes out to be of Rs. 200. Now if the cost of 1 kg of tomato is Rs. 50 and 1 kg of potato is Rs. 20, then answer the following questions.

(i) Which of the following equations represent the total cost.

(a) 5x – 2y = 20

(b) 5y + 2x = 20

(c) 5x + 2y = 20

(d) 2x + 5y = 20

(ii) If Anil bought ‘x’ kgs of tomato and 2.5 kgs. of potato, then find the value of ‘x’.

(a) 5

(b) 2

(c) 3

(d) 4

(iii) If Anil bought ‘2’ kgs of tomato and ‘y’ kgs of potato, then find the value of ‘y’.

(a) 5

(b) 2

(c) 3

(d) 4

(iv) The graph of 5x + 2y = 20 cuts x-axis at the point.

(a) (10, 0)

(b) (4, 0)

(c) (0, 0)

(d) it is parallel to x-axis

(v) The graph of 5x + 2y = 20 cuts y-axis at the point.

(a) (0, 10)

(b) (0, 4)

(c) (0, 0)

(d) it is parallel to y-axis

**Answers**

(i) C (ii) C (iii) A (iv) B (v) A

**Check Detailed Solution**

## Click to Check Detailed Solution

(i) The equation representing the total cost is:(c) 5x + 2y = 20

To find this, we need to consider that the cost of ‘x’ kgs of tomatoes is 50x, and the cost of ‘y’ kgs of potatoes is 20y. The total cost is the sum of these two, which comes out to be Rs. 200.

(ii) If Anil bought ‘x’ kgs of tomato and 2.5 kgs of potato, then the equation representing the total cost would be:

Total cost = (Cost of ‘x’ kgs of tomato) + (Cost of 2.5 kgs of potato)

Total cost = (50x) + (20 * 2.5)

Total cost = 50x + 50

Given that the total cost is Rs. 200, we can set up the equation:

50x + 50 = 200

Subtract 50 from both sides:

50x = 150

Now, divide both sides by 50:

x = 3

So, the value of ‘x’ is 3. Hence, the answer is (c) 3.

(iii) If Anil bought 2 kgs of tomato and ‘y’ kgs of potato, then the equation representing the total cost would be:

Total cost = (Cost of 2 kgs of tomato) + (Cost of ‘y’ kgs of potato)

Total cost = (50 * 2) + (20y)

Total cost = 100 + 20y

Given that the total cost is Rs. 200, we can set up the equation:

100 + 20y = 200

Subtract 100 from both sides:

20y = 100

Now, divide both sides by 20:

y = 5

So, the value of ‘y’ is 5. Hence, the answer is (a) 5.

(iv) To find where the graph of the equation 5x + 2y = 20 cuts the x-axis, we set y = 0 and solve for x:

5x + 2(0) = 20

5x = 20

Divide both sides by 5:

x = 4

So, the graph cuts the x-axis at the point (4, 0). Hence, the answer is (b) (4, 0).

(v) To find where the graph of the equation 5x + 2y = 20 cuts the y-axis, we set x = 0 and solve for y:

5(0) + 2y = 20

2y = 20

Divide both sides by 2:

y = 10

So, the graph cuts the y-axis at the point (0, 10). Hence, the answer is (a) (0, 10).

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Where are the answers?

Answer key

(i)(c) 5x + 2y = 20

(ii)(c) 3

(iii)(a) 5

(iv)(b) (4, 0)

(v)(a) (0, 10)

Hlo sir I have doubt

kindly solve ii and iii part