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:

- Always separate two ratios: the \textit{mixing ratio} and the \textit{cost ratio}.
- Multiply the quantity ratio by the cost ratio to find effective costs.
- Use proportional distribution when total cost is given.

Answer 1

The Correct Option is A

Step 1: The mixing ratio of sand : cement = \(3 : 1\).
This means if we take 3 units of sand, we take 1 unit of cement.
Step 2: The cost ratio of sand : cement = \(1 : 2\).
Let cost of 1 unit of sand = \(x\).
Then cost of 1 unit of cement = \(2x\).
Step 3: Total cost of mixture = (3 units of sand + 1 unit of cement).
= \(3 \times x + 1 \times (2x) = 3x + 2x = 5x\).
Step 4: It is given that total cost = \(\rupee 1000\).
So, \(5x = 1000 \Rightarrow x = 200\).
Step 5: Cost of cement used = \(2x = 2 \times 200 = \rupee 400\).
\[\boxed{400}\]