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How many units of sand are needed if 110 units of concrete are to be mixed in the ratio 1:1.5:3?
- a)50 units
- b)40 units
- c)60 units
- d)30 units
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
How many units of sand are needed if 110 units of concrete are to be m...
Understanding the Ratio
To solve the problem, we need to first understand the given ratio of concrete, sand, and gravel, which is 1 : 1.5 : 3. This means for every 1 part of concrete, there are 1.5 parts of sand and 3 parts of gravel.
Calculating Total Parts
- The total parts in the ratio can be calculated as follows:
- Concrete: 1 part
- Sand: 1.5 parts
- Gravel: 3 parts
- Total parts = 1 + 1.5 + 3 = 5.5 parts
Calculating the Quantity of Each Component
Now, we know that 110 units of concrete corresponds to 1 part of the total ratio. Therefore, we can find out how many units each part represents:
- Each part = 110 units (concrete) / 1 (part of concrete) = 110 units
Next, we can calculate the amount of sand needed:
- Sand = 1.5 parts × 110 units/part = 165 units
Finding the Proportion of Sand
Since we need to find how much sand is required in relation to the concrete's total volume (110 units), we can use the following proportion:
- Proportion of sand = (1.5 / 5.5) × Total units (110 units)
Calculating this gives:
- Sand = (1.5 / 5.5) × 110 = 30 units
Conclusion
However, it seems there was a misunderstanding in the initial setup. Given a total of 110 units for concrete and the ratios, the resulting calculation indeed leads us to the correct amount of sand needed, which is 55 units.
Thus, the correct answer is option 'B' - 55 units of sand are required.
To solve the problem, we need to first understand the given ratio of concrete, sand, and gravel, which is 1 : 1.5 : 3. This means for every 1 part of concrete, there are 1.5 parts of sand and 3 parts of gravel.
Calculating Total Parts
- The total parts in the ratio can be calculated as follows:
- Concrete: 1 part
- Sand: 1.5 parts
- Gravel: 3 parts
- Total parts = 1 + 1.5 + 3 = 5.5 parts
Calculating the Quantity of Each Component
Now, we know that 110 units of concrete corresponds to 1 part of the total ratio. Therefore, we can find out how many units each part represents:
- Each part = 110 units (concrete) / 1 (part of concrete) = 110 units
Next, we can calculate the amount of sand needed:
- Sand = 1.5 parts × 110 units/part = 165 units
Finding the Proportion of Sand
Since we need to find how much sand is required in relation to the concrete's total volume (110 units), we can use the following proportion:
- Proportion of sand = (1.5 / 5.5) × Total units (110 units)
Calculating this gives:
- Sand = (1.5 / 5.5) × 110 = 30 units
Conclusion
However, it seems there was a misunderstanding in the initial setup. Given a total of 110 units for concrete and the ratios, the resulting calculation indeed leads us to the correct amount of sand needed, which is 55 units.
Thus, the correct answer is option 'B' - 55 units of sand are required.
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Community Answer
How many units of sand are needed if 110 units of concrete are to be m...
Total parts = 1 + 1.5 + 3 = 5.5.
Fraction of sand = 1.5 / 5.5 = 3/11.
Sand required = 110 × (3/11) = 10 × 3 = 30 units.
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