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There are three containers - M, Wand H - of equal capacities, containing milk, water and honey respectively. Each container is filled upto 75% of its capacity. Now, W is topped up to its brim (i.e., filled completely), with the contents of M. The contents of Ware then thoroughly mixed. Then H is topped up to its brim with the contents of W. The contents of Hare then thoroughly mixed. Finally, the contents of Hare used to fill M again up to 75% of its capacity. Which among the following statements is true regarding m, w and h, which are the respective final concentrations of milk in M, water in Wand honey in H?
  • a)
    m < w="" />
  • b)
    w > h > m
  • c)
    m = w = h
  • d)
    None of the above
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
There are three containers - M, Wand H - of equal capacities, contain...
Given information:
- Containers M, W, and H have equal capacities.
- Each container is filled up to 75% of its capacity.
- Container W is topped up with the contents of M.
- The contents of W are thoroughly mixed.
- Container H is topped up with the contents of W.
- The contents of H are thoroughly mixed.
- The contents of H are used to fill M again up to 75% of its capacity.

Final concentrations:
Let's assume the initial capacities of M, W, and H are M0, W0, and H0 respectively. After each step, the concentration of each substance in the containers changes.

1. M is topped up with the contents of W:
- The volume of milk in M: M0 + (W0 * 0.75)
- The volume of water in M: 0.75 * W0
- The volume of honey in M: 0.75 * H0

2. W is topped up with the contents of M:
- The volume of milk in W: 0.75 * (M0 + (W0 * 0.75))
- The volume of water in W: W0 + (0.75 * W0)
- The volume of honey in W: 0.75 * H0

3. H is topped up with the contents of W:
- The volume of milk in H: 0.75 * (0.75 * (M0 + (W0 * 0.75)))
- The volume of water in H: 0.75 * (W0 + (0.75 * W0))
- The volume of honey in H: H0 + (0.75 * H0)

4. H is used to fill M again up to 75% of its capacity:
- The volume of milk in M: 0.75 * (0.75 * (0.75 * (M0 + (W0 * 0.75))))
- The volume of water in M: 0.75 * (W0 + (0.75 * W0))
- The volume of honey in M: 0.75 * (H0 + (0.75 * H0))

Final concentrations:
- Concentration of milk in M: (0.75 * (0.75 * (0.75 * (M0 + (W0 * 0.75))))) / (0.75 * (W0 + (0.75 * W0)))
- Concentration of water in W: (W0 + (0.75 * W0)) / (0.75 * (M0 + (W0 * 0.75)))
- Concentration of honey in H: (H0 + (0.75 * H0)) / (0.75 * (W0 + (0.75 * W0)))

Comparison of final concentrations:
- Concentration of milk in M > Concentration of water in W > Concentration of honey in H

Therefore, the correct answer is option 'A': m > w > h.
Free Test
Community Answer
There are three containers - M, Wand H - of equal capacities, contain...
Each vessel is filled to 3/4 of its capacity, .. It is convenient to take the capacity as 4 units. Each vessel would have 3 units, In the second step, one-fourth the contents of Ware transferred to H i.e., 1/4 units of milk and 3/4 units of water.
It is convenient to take the capacity of each container as 16 units, The quantities at different stages are tabulated below.
m = 8.2516 , w = 916 , h = 916 or m < w="" />
Hence, the correct option is (a).
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There are three containers - M, Wand H - of equal capacities, containing milk, water and honey respectively. Each container is filled upto 75% of its capacity. Now, W is topped up to its brim (i.e., filled completely), with the contents of M. The contents of Ware then thoroughly mixed. Then H is topped up to its brim with the contents of W. The contents of Hare then thoroughly mixed. Finally, the contents of Hare used to fill M again up to 75% of its capacity. Which among the following statements is true regarding m, w and h, which are the respective final concentrations of milk in M, water in Wand honey in H?a)m b)w > h > mc)m = w = hd)None of the aboveCorrect answer is option 'A'. Can you explain this answer?
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