Discussion
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?
Answer: A
The cement costs 400 rupees.
Take 3 parts of sand and 1 part of cement. If one part of sand costs 1 unit, one part of cement costs 2 units, so the costs are
\[ \begin{aligned} \text{sand} &= 3 \times 1 = 3 \\ \text{cement} &= 1 \times 2 = 2 \end{aligned} \]
The cost ratio is therefore 3 : 2, and cement takes 2/5 of the total: 2/5 × 1000 = 400 rupees.
600 is the sand’s share, not the cement’s. 200 is the value of a single cost unit, forgetting that the cement accounts for two of the five. 800 cannot be right, since it would leave only 200 rupees for three times as much sand at half the unit price.
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