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40 kg of crystals are graded into 3 sizes: small, medium and large. The ratio by mass of large to medium to small crystals is 4 : 3 : 1. There are 15 large crystals per kg. The total numbers of large crystals are
  • a)
    525
  • b)
    560 
  • c)
    300
  • d)
    570 
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
40 kg of crystals are graded into 3 sizes: small, medium and large. Th...
Given:
- 40 kg of crystals are graded into 3 sizes: small, medium and large.
- The ratio by mass of large to medium to small crystals is 4 : 3 : 1.
- There are 15 large crystals per kg.

To find: The total numbers of large crystals.

Solution:

1. Find the total mass of crystals for each size:
- Let the mass of small crystals be x kg.
- Then, the mass of medium crystals is 3x kg (as per the given ratio).
- And the mass of large crystals is 4x kg (as per the given ratio).

- Therefore, x + 3x + 4x = 40 kg (total mass of crystals)
- Simplifying, we get 8x = 40 kg
- Therefore, x = 5 kg.

- Hence, the mass of small crystals is 5 kg, medium crystals is 15 kg and large crystals is 20 kg.

2. Find the total number of large crystals:
- Given, there are 15 large crystals per kg.
- Therefore, the total number of large crystals is 15 x 20 = 300.

Therefore, the total number of large crystals is 300.

Hence, the correct option is (c) 300.
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Community Answer
40 kg of crystals are graded into 3 sizes: small, medium and large. Th...
300
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