Question

To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand and that of cement are in the ratio of 1:2. If the total cost of sand and cement to construct the wall is 1000 rupees, then what is the cost (in rupees) of cement used?

• A. 400
• B. 600
• C. 800
• D. 200

Hint:

When items are mixed in a ratio and have different unit costs, allocate total cost using “quantity \(\times\) unit-cost” as weights.

Answer 1

The Correct Option is A

Let unit costs be \(c_s:c_c=1:2\). Quantities mixed are \(q_s:q_c=3:1\). Cost share \(\propto\) (quantity)\(\times\)(unit cost). Hence \[ \text{Sand share} : \text{Cement share}=(3\times 1):(1\times 2)=3:2. \] Total cost is 1000, so cement’s part is \[ \frac{2}{3+2}\times 1000=\frac{2}{5}\times 1000=400. \] \[ \boxed{400} \]