GATE CH 2023 | GA Question: 7

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. $200$

Answer 1

Cost of sand/cost of cement = ½

Cost of sand = 1/2 cost of cement

Total cost = cost of sand + cost of cement

     1000 = 1/2 cost of cement + cost of cement

1000×2/3 = cost of cement

Cost of cement is 600rs

Answer 2

Let cost ratio be 1:2

Assuming x and 2x will be the cost of sand and cement respectively.

Ratio of quantity be 3y and 2y for sand and cement

So, the cost of sand = 3xy

And cost of cement= 2xy

Total cost is Rs 1000

Therefore,

x.3y+2xy= 1000

5xy=1000

xy= 200

So, the cost of cement =2xy

2(200)

= Rs 400