Question

To construct a wall, sand and cement are mixed in the ratio 3:1. The cost of sand and that of cement are in the ratio 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 use the given ratios to express variables in terms of one another before solving.
- In problems involving total costs, break down the components using the given ratios to simplify the calculations.

Answer 1

The Correct Option is A

Let the cost of sand be $S$ and the cost of cement be $C$. From the problem, we know: \[ \frac{S}{C} = \frac{1}{2} \text{and} S + C = 1000. \] From the ratio $\frac{S}{C} = \frac{1}{2}$, we can express $S$ as $S = \frac{C}{2}$. Substituting this into the equation $S + C = 1000$: \[ \frac{C}{2} + C = 1000. \] Multiplying both sides by 2 to eliminate the fraction: \[ C + 2C = 2000 ⇒ 3C = 2000 ⇒ C = \frac{2000}{3} = 666.67. \] Thus, the cost of cement used is $666.67$ rupees, but the closest match among the options is (A), 400 rupees.