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Bob makes dry concrete by mixing cement, sand and stone in the ratio 1 : 2 : 3 by weight - OCR - GCSE Maths - Question 18 - 2019 - Paper 1
Question 18
Bob makes dry concrete by mixing cement, sand and stone in the ratio 1 : 2 : 3 by weight. He buys the cement, sand and stone in bags as shown in this table. | Weigh... show full transcript
Worked Solution & Example Answer:Bob makes dry concrete by mixing cement, sand and stone in the ratio 1 : 2 : 3 by weight - OCR - GCSE Maths - Question 18 - 2019 - Paper 1
Step 1
Show that Bob buys 500 kg of sand.
Answer
In order to find the total amounts of materials Bob needs, we start with the ratio of cement, sand, and stone, which is 1:2:3.
1. Calculate the total parts in the ratio:
The total parts = 1 + 2 + 3 = 6 parts.
2. Calculate the total weight needed for 50 bags:
Each bag weighs 30 kg, thus:
3. Calculate the weight of each material:
Using the ratio, each material's weight can be calculated as follows:
- Cement: rac{1}{6} imes 1500 = 250 ext{ kg}
- Sand: rac{2}{6} imes 1500 = 500 ext{ kg}
- Stone: rac{3}{6} imes 1500 = 750 ext{ kg}
Conclusion:
Thus, the weight of sand purchased by Bob is 500 kg, as required.
Step 2
Calculate Bob's percentage profit.
Answer
To find Bob's percentage profit, we first need to determine his total cost for the materials.
1. Calculate the cost of each material:
-
Cement: 25 kg at £5.50 per bag:
- Number of bags = rac{250 ext{ kg}}{25 ext{ kg/bag}} = 10 ext{ bags}
- Cost of cement = 10 bags × £5.50 = £55
-
Sand: 20 kg at £2.00 per bag:
- Number of bags = rac{500 ext{ kg}}{20 ext{ kg/bag}} = 25 ext{ bags}
- Cost of sand = 25 bags × £2.00 = £50
-
Stone: 15 kg at £3.90 per bag:
- Number of bags = rac{750 ext{ kg}}{15 ext{ kg/bag}} = 50 ext{ bags}
- Cost of stone = 50 bags × £3.90 = £195
2. Calculate the total cost:
Total cost = £55 (cement) + £50 (sand) + £195 (stone) = £300
3. Calculate the profit:
Profit = Selling price - Cost price = £396 - £300 = £96
4. Calculate the percentage profit:
Percentage profit is given by:
ext{Percentage Profit} = rac{ ext{Profit}}{ ext{Cost Price}} imes 100 = rac{96}{300} imes 100 eq 32 ext{%}Conclusion:
Therefore, Bob's percentage profit is 32%.