GATE 2023 PH – Question 7
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?
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: (A) 400
Explanation
**Step 1: quantities.** Sand : cement by quantity is $3:1$. Suppose the wall uses 3 units of sand and 1 unit of cement.
**Step 2: prices.** The cost per unit of sand to the cost per unit of cement is $1:2$. Take sand at 1 per unit and cement at 2 per unit.
**Step 3: costs.**
- Sand: $3\times1=3$
- Cement: $1\times2=2$
- Total: $5$
**Step 4: cement share.** Cement is $\dfrac25$ of the total cost:
$$\text{Cost of cement}=\frac25\times1000=\mathbf{₹400}.$$