Class 8 Direct Proportion Case Study with Answers

Class 8 Direct Proportion Case Study with Answers

Class 8 Direct Proportion Case Study with Answers

The Class 8 Direct Proportion Case Study with Answers helps students understand how quantities increase or decrease together in a real-life context. Moreover, each case study includes clear explanations that make learning easier. These problems guide students to identify relationships and apply direct proportion correctly.

Why These Case Studies Are Helpful

These worksheets improve analytical thinking and enhance conceptual clarity. Furthermore, the step-by-step answers show students how to approach each question with confidence. As a result, learners build a strong foundation for advanced math topics.

How Students Should Practice

Students should read the situation carefully and observe how values change. Additionally, applying the direct proportion formula step by step helps them gain accuracy and speed for exams.

Case Study 4: Class 8 Direct Proportion Case Study with Answers

A group of schools jointly organises a mid-term cultural festival and plans to provide snack boxes to all attendees. The organising committee prepares a standard snack mix where the ratio of **roasted gram : roasted peanuts : dried fruit is 7 : 2 : 1 by weight**. On day one, they prepared **720 snack boxes** using **84 kilograms of roasted gram**, **24 kilograms of roasted peanuts** and **12 kilograms of dried fruit**.

During preparations they faced three practical constraints: (i) one of the peanut suppliers can deliver only half the usual supply, (ii) the number of boxes ordered by participating schools may increase, and (iii) volunteer cooks may vary in number across shifts. The committee must use **ratios** to check whether day-one quantities match the standard recipe, the **unitary method** for ingredient-per-box calculations, **direct proportion** to scale up ingredients when boxes increase, and **inverse proportion** to compute change in preparation time when volunteers change. In addition they must divide the total ingredient cost among three participating schools in proportion to the number of boxes each school requested.

1. Do the quantities used on day one (84 kg roasted gram, 24 kg peanuts, 12 kg dried fruit) match the standard recipe ratio 7 : 2 : 1?
Solution:

The ratio of quantities used is $84 : 24 : 12$. The greatest common divisor is 12. Dividing each term by 12:

\(\frac{84}{12} : \frac{24}{12} : \frac{12}{12} = 7 : 2 : 1\)

Thus, the quantities exactly match the standard recipe ratio.

Correct Answer: (a)

2. Using the unitary method, how much roasted gram is used per snack box on day one?
Solution:

Total roasted gram = 84 kg for 720 boxes. Roasted gram per box is:

\(\frac{84}{720} = \frac{7}{60} \approx 0.116\overline{6}\text{ kg}\)

Rounding to two decimal places gives 0.12 kg.

Correct Answer: (a)

3. If the number of requested snack boxes increases from 720 to 900 and the recipe ratio remains the same, how many kilograms of roasted peanuts are required?
Solution:

This is a direct proportion. Peanuts used for 720 boxes = 24 kg. Peanuts per box is $24/720 = 1/30$ kg.

For 900 boxes, required peanuts:

\(900 \times \frac{1}{30} = 30\text{ kg}\)

Correct Answer: (a)

4. Five volunteers take 6 hours to fill and pack 360 snack boxes. If the organising committee wants the same work done in 3 hours, how many volunteers are required (assume inverse proportion)?
Solution:

Work is fixed, so time is inversely proportional to the number of volunteers. Let $v$ be the required number of volunteers. (Volunteers $\times$ Time) is constant:

\(5 \times 6 = v \times 3 \quad\Rightarrow\quad v = \frac{30}{3} = 10\)

Thus, 10 volunteers are required.

Correct Answer: (b)

5. The total ingredient cost for 720 boxes is Rs. 14,400. Three schools A, B and C ordered 200, 300 and 220 boxes respectively. The cost is to be shared in direct proportion to the number of boxes ordered. How much should School B pay?
Solution:

Total boxes ordered = $200 + 300 + 220 = 720$ boxes.

Cost per box = $\frac{\text{Total Cost}}{\text{Total Boxes}} = \frac{14400}{720} = 20\text{ Rs. per box}$.

School B ordered 300 boxes, so its share is:

\(300 \times 20 = 6000\text{ Rs.}\)

Since the cost per box is an exact integer (Rs. 20), the share is exactly Rs. 6,000.

Correct Answer: (c)

Review your answers and solutions below:

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