Question

To construct a wall, sand and cement are mixed in the ratio \(3:1\). The costs per unit of sand and cement are in the ratio \(1:2\). If the total cost of sand and cement is ₹~1000, what is the cost (in rupees) of cement used?

• A. 400
• B. 600
• C. 800
• D. 200

Hint:

When mixture and price ratios are given, assign variables to quantity ratio and unit-price ratio; the total cost becomes a simple sum of "quantity \(\times\) unit price" terms.

Answer 1

The Correct Option is A

Step 1: Let variables represent quantity and unit costs.
Let the quantities be \(3x\) (sand) and \(x\) (cement).
Let unit cost of sand be \(c\); then unit cost of cement is \(2c\).

Step 2: Write the total cost equation.
Total cost \(=\) \(3x\cdot c + x\cdot 2c = 5cx = ₹~1000\).
Hence \(cx = ₹~200\).

Step 3: Compute cement cost.
Cement cost \(=\) quantity \(\times\) unit cost \(= x\cdot 2c = 2(cx) = 2\times ₹~200 = ₹~400\).

Final Answer:
\[ \boxed{₹~400} \]