Understanding the Cost Calculation Problem

This question involves finding the cost of a certain quantity of walnuts based on a chain of cost relationships between different items: rice, pulse, tea, and walnuts. We start with the known cost of rice and use the given equivalences to find the cost of pulse, then tea, and finally walnuts.

Breaking Down the Cost Relationships

Let's list the given relationships:

• Cost of 3 kg of rice is ₹180.
• Cost of 8 kg of rice is equal to the cost of 5 kg of pulse.
• Cost of 15 kg of pulse is equal to the cost of 2 kg of tea.
• Cost of 3 kg of tea is equal to the cost of 6 kg of walnuts.

We need to find the cost of 10 kg of walnuts.

Step-by-Step Cost Calculation

We will calculate the cost of 1 kg of each item sequentially, starting with rice.

Step 1: Find the cost of 1 kg of rice.

Given that the cost of 3 kg of rice is ₹180.

Cost of 1 kg of rice \( = \frac{\text{Total cost of rice}}{\text{Quantity of rice}} \)

Cost of 1 kg of rice \( = \frac{180}{3} \text{ ₹} \)

Cost of 1 kg of rice \( = 60 \text{ ₹} \)

Step 2: Find the cost of 8 kg of rice.

Cost of 8 kg of rice \( = 8 \times \text{Cost of 1 kg of rice} \)

Cost of 8 kg of rice \( = 8 \times 60 \text{ ₹} \)

Cost of 8 kg of rice \( = 480 \text{ ₹} \)

Step 3: Find the cost of 5 kg of pulse.

We are given that the cost of 8 kg of rice is equal to the cost of 5 kg of pulse.

Cost of 5 kg of pulse \( = \text{Cost of 8 kg of rice} \)

Cost of 5 kg of pulse \( = 480 \text{ ₹} \)

Step 4: Find the cost of 1 kg of pulse.

Cost of 1 kg of pulse \( = \frac{\text{Total cost of pulse}}{\text{Quantity of pulse}} \)

Cost of 1 kg of pulse \( = \frac{480}{5} \text{ ₹} \)

Cost of 1 kg of pulse \( = 96 \text{ ₹} \)

Step 5: Find the cost of 15 kg of pulse.

Cost of 15 kg of pulse \( = 15 \times \text{Cost of 1 kg of pulse} \)

Cost of 15 kg of pulse \( = 15 \times 96 \text{ ₹} \)

Cost of 15 kg of pulse \( = 1440 \text{ ₹} \)

Step 6: Find the cost of 2 kg of tea.

We are given that the cost of 15 kg of pulse is equal to the cost of 2 kg of tea.

Cost of 2 kg of tea \( = \text{Cost of 15 kg of pulse} \)

Cost of 2 kg of tea \( = 1440 \text{ ₹} \)

Step 7: Find the cost of 1 kg of tea.

Cost of 1 kg of tea \( = \frac{\text{Total cost of tea}}{\text{Quantity of tea}} \)

Cost of 1 kg of tea \( = \frac{1440}{2} \text{ ₹} \)

Cost of 1 kg of tea \( = 720 \text{ ₹} \)

Step 8: Find the cost of 3 kg of tea.

Cost of 3 kg of tea \( = 3 \times \text{Cost of 1 kg of tea} \)

Cost of 3 kg of tea \( = 3 \times 720 \text{ ₹} \)

Cost of 3 kg of tea \( = 2160 \text{ ₹} \)

Step 9: Find the cost of 6 kg of walnuts.

We are given that the cost of 3 kg of tea is equal to the cost of 6 kg of walnuts.

Cost of 6 kg of walnuts \( = \text{Cost of 3 kg of tea} \)

Cost of 6 kg of walnuts \( = 2160 \text{ ₹} \)

Step 10: Find the cost of 1 kg of walnut.

Cost of 1 kg of walnut \( = \frac{\text{Total cost of walnuts}}{\text{Quantity of walnuts}} \)

Cost of 1 kg of walnut \( = \frac{2160}{6} \text{ ₹} \)

Cost of 1 kg of walnut \( = 360 \text{ ₹} \)

Step 11: Find the cost of 10 kg of walnuts.

Cost of 10 kg of walnuts \( = 10 \times \text{Cost of 1 kg of walnut} \)

Cost of 10 kg of walnuts \( = 10 \times 360 \text{ ₹} \)

Cost of 10 kg of walnuts \( = 3600 \text{ ₹} \)

So, the cost of 10 kg of walnuts is ₹3600.

Summary of Costs per kg

Conclusion

By following the chain of cost relationships given in the problem, we calculated the cost per kg for each item and then determined the final cost of 10 kg of walnuts.

Revision Table: Key Cost Relationships

Reviewing the relationships helps reinforce the problem structure:

• Rice cost leads to Pulse cost (via 8kg rice = 5kg pulse)
• Pulse cost leads to Tea cost (via 15kg pulse = 2kg tea)
• Tea cost leads to Walnuts cost (via 3kg tea = 6kg walnuts)

Additional Information: Ratio and Proportion in Cost Problems

This type of problem can also be approached using ratios and proportions. For example, if 3 kg of rice costs ₹180, the ratio of cost to quantity is constant (\( \frac{180}{3} \)). We use this proportionality to find the cost of other quantities. Similarly, the relationships between different items (like 8 kg rice = 5 kg pulse) imply a ratio between their costs per kg.