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?
Options:
(A) 400
(B) 600
(C) 800
(D) 200
Official Answer Key:
A
Step-by-Step Solution & Explanation
Let the quantity of sand = 3k, cement = k (mixing ratio 3:1). Let unit cost of sand = c, unit cost of cement = 2c (cost ratio 1:2). Cost of sand = 3k×c = 3kc; cost of cement = k×2c = 2kc. Total cost = 3kc+2kc = 5kc = 1000 ⇒ kc = 200. Cost of cement = 2kc = 400. Answer: (A) 400. *Distractor note:* (C) 800 results from mixing up which ratio (mixing vs cost) applies to which quantity.
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