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From a container of Milk, a thief has stolen 16 litres of Milk and replaced it with same quantity of water. He repeated the same process again two more times. Then ratio of Milk and Water is 3375:1538. Then what is the initial amount of Milk in the container?
- a)120 Litre
- b)136 Litre
- c)142 Litre
- d)154 Litre
- e)None
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
From a container of Milk, a thief has stolen 16 litres of Milk and rep...
3375x = 4913x(1-16/y) 3
15/17 = 1-16/y
y = 136
15/17 = 1-16/y
y = 136
Most Upvoted Answer
From a container of Milk, a thief has stolen 16 litres of Milk and rep...
Initial amount of milk in the container = x litres
The thief steals 16 litres of milk and replaces it with the same quantity of water. This process is repeated three times.
After the first replacement:
Milk remaining = (x - 16) litres
Water added = 16 litres
After the second replacement:
Milk remaining = (x - 16) - 16 = (x - 32) litres
Water added = 16 + 16 = 32 litres
After the third replacement:
Milk remaining = (x - 32) - 16 = (x - 48) litres
Water added = 32 + 16 = 48 litres
Given that the ratio of milk to water is 3375:1538, we can set up the equation:
Milk remaining / Water added = 3375/1538
(x - 48) / 48 = 3375/1538
Cross-multiplying, we get:
1538(x - 48) = 3375 * 48
1538x - 73824 = 162000
1538x = 162000 + 73824
1538x = 235824
x = 235824 / 1538
x ≈ 153.38
Therefore, the initial amount of milk in the container is approximately 153.38 litres.
However, since the options provided are in whole numbers, we can round up the answer to the nearest whole number.
Hence, the initial amount of milk in the container is approximately 154 litres.
Therefore, the correct answer is option (d) 154 litres.
The thief steals 16 litres of milk and replaces it with the same quantity of water. This process is repeated three times.
After the first replacement:
Milk remaining = (x - 16) litres
Water added = 16 litres
After the second replacement:
Milk remaining = (x - 16) - 16 = (x - 32) litres
Water added = 16 + 16 = 32 litres
After the third replacement:
Milk remaining = (x - 32) - 16 = (x - 48) litres
Water added = 32 + 16 = 48 litres
Given that the ratio of milk to water is 3375:1538, we can set up the equation:
Milk remaining / Water added = 3375/1538
(x - 48) / 48 = 3375/1538
Cross-multiplying, we get:
1538(x - 48) = 3375 * 48
1538x - 73824 = 162000
1538x = 162000 + 73824
1538x = 235824
x = 235824 / 1538
x ≈ 153.38
Therefore, the initial amount of milk in the container is approximately 153.38 litres.
However, since the options provided are in whole numbers, we can round up the answer to the nearest whole number.
Hence, the initial amount of milk in the container is approximately 154 litres.
Therefore, the correct answer is option (d) 154 litres.
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