Question

Sand and cement are mixed in the ratio \(3:1\). Cost ratio of sand to cement is \(1:2\). Total cost of sand and cement is \(\,1000\) rupees. Find the cost of cement used.

• A. 400
• B. 600
• C. 800
• D. 200

Hint:

Always separate "quantity ratio" and "cost ratio." Multiply quantity × unit cost to avoid mistakes. Recheck totals to confirm.

Answer 1

The Correct Option is B

Step 1: Represent quantities.
Sand : Cement (quantity) = \(3:1\). Let sand = 3 units, cement = 1 unit.

Step 2: Represent costs.
Cost per unit of sand : cement = \(1:2\). Let cost of sand per unit = \(x\), then cement per unit = \(2x\).

Step 3: Total cost calculation.
Total cost = \((3 \times x) + (1 \times 2x) = 3x + 2x = 5x\). Given: \(5x = 1000 \;\Rightarrow\; x = 200\).

Step 4: Cost of cement.
Cement = \(1\) unit \(\times\) \(2x\) = \(2 \times 200 = 400\). Wait, check carefully: Cement quantity is 1 unit, but its cost per unit = \(2x = 400\). So cement cost = \(400\). Recheck carefully.
Sand cost = \(3 \times 200 = 600\). Cement cost = 400. Total = 1000. Matches given.

Final Answer:
\[ \boxed{400} \]