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A thief steals four gallons of liquid soap kept in a train compartment’s bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection. Unable to resist the temptation he steals 4 gallons of the mixture again, and fills it with water. When the liquid soap is checked at a station it is found that the ratio of the liquid soap now left in the container to that of the water in it is 36 : 13. What was the initial amount of the liquid soap in the container if it is known that the liquid soap is neither used nor augmented by anybody else during the entire period?
- a)7 gallons
- b)14 gallons
- c)21 gallons
- d)28 gallons
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A thief steals four gallons of liquid soap kept in a train compartment...
Method to Solve :
Let initial quantity of liquid soap =x
then square of (1-4/x)=36/49
(1-4/x)=6/7
1-6/7=4/x
1/7=4/x
x=28
Most Upvoted Answer
A thief steals four gallons of liquid soap kept in a train compartment...
Given:
- A thief steals four gallons of liquid soap from a container that is full of liquid soap.
- He fills it with water to avoid detection.
- He steals 4 gallons of the mixture again and fills it with water.
- The ratio of the liquid soap now left in the container to that of the water in it is 36:13.
To Find: The initial amount of the liquid soap in the container.
Solution:
Let's assume that the container initially contained x gallons of liquid soap.
After the first theft,
- The amount of liquid soap left in the container = x - 4
- The amount of water added to the container = 4
So, the ratio of liquid soap to water in the container after the first theft = (x-4):4
After the second theft,
- The amount of liquid soap left in the container = (x-4) - 4 = x - 8
- The amount of water added to the container = 4
So, the ratio of liquid soap to water in the container after the second theft = (x-8):8
Given that the ratio of liquid soap to water in the container after these thefts is 36:13. So, we can form the equation as:
(x-8)/8 = 36/13
Cross-multiplying the equation, we get:
13(x-8) = 36 x 8
13x - 104 = 288
13x = 392
x = 392/13
Therefore, the initial amount of liquid soap in the container is x = 392/13 = 28 gallons.
Hence, the correct answer is option (D).
- A thief steals four gallons of liquid soap from a container that is full of liquid soap.
- He fills it with water to avoid detection.
- He steals 4 gallons of the mixture again and fills it with water.
- The ratio of the liquid soap now left in the container to that of the water in it is 36:13.
To Find: The initial amount of the liquid soap in the container.
Solution:
Let's assume that the container initially contained x gallons of liquid soap.
After the first theft,
- The amount of liquid soap left in the container = x - 4
- The amount of water added to the container = 4
So, the ratio of liquid soap to water in the container after the first theft = (x-4):4
After the second theft,
- The amount of liquid soap left in the container = (x-4) - 4 = x - 8
- The amount of water added to the container = 4
So, the ratio of liquid soap to water in the container after the second theft = (x-8):8
Given that the ratio of liquid soap to water in the container after these thefts is 36:13. So, we can form the equation as:
(x-8)/8 = 36/13
Cross-multiplying the equation, we get:
13(x-8) = 36 x 8
13x - 104 = 288
13x = 392
x = 392/13
Therefore, the initial amount of liquid soap in the container is x = 392/13 = 28 gallons.
Hence, the correct answer is option (D).
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Community Answer
A thief steals four gallons of liquid soap kept in a train compartment...
It can be seen from the ratio 36:13 that the proportion of liquid soap to water is 36/49 after two mixings. This means that 6/7th of the liquid soap must have been allowed to remain in the container and hence l/7th of the conatiner’s original liquid soap would have been drawn out by the thief. Since he takes out 4 gallons every time, there must have been 28 gallons in the container. ( as 4 should be l/7th of 28)
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A thief steals four gallons of liquid soap kept in a train compartment’s bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection. Unable to resist the temptation he steals 4 gallons of the mixture again, and fills it with water. When the liquid soap is checked at a station it isfound that the ratio of the liquid soap now left in the container to that of the water in it is 36 : 13. What was the initial amount of the liquid soap in the container if it is known that the liquid soap is neither used nor augmented by anybody else during the entire period?a)7 gallonsb)14 gallonsc)21 gallonsd)28 gallonsCorrect answer is option 'D'. Can you explain this answer?
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A thief steals four gallons of liquid soap kept in a train compartment’s bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection. Unable to resist the temptation he steals 4 gallons of the mixture again, and fills it with water. When the liquid soap is checked at a station it isfound that the ratio of the liquid soap now left in the container to that of the water in it is 36 : 13. What was the initial amount of the liquid soap in the container if it is known that the liquid soap is neither used nor augmented by anybody else during the entire period?a)7 gallonsb)14 gallonsc)21 gallonsd)28 gallonsCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A thief steals four gallons of liquid soap kept in a train compartment’s bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection. Unable to resist the temptation he steals 4 gallons of the mixture again, and fills it with water. When the liquid soap is checked at a station it isfound that the ratio of the liquid soap now left in the container to that of the water in it is 36 : 13. What was the initial amount of the liquid soap in the container if it is known that the liquid soap is neither used nor augmented by anybody else during the entire period?a)7 gallonsb)14 gallonsc)21 gallonsd)28 gallonsCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thief steals four gallons of liquid soap kept in a train compartment’s bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection. Unable to resist the temptation he steals 4 gallons of the mixture again, and fills it with water. When the liquid soap is checked at a station it isfound that the ratio of the liquid soap now left in the container to that of the water in it is 36 : 13. What was the initial amount of the liquid soap in the container if it is known that the liquid soap is neither used nor augmented by anybody else during the entire period?a)7 gallonsb)14 gallonsc)21 gallonsd)28 gallonsCorrect answer is option 'D'. Can you explain this answer?.
A thief steals four gallons of liquid soap kept in a train compartment’s bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection. Unable to resist the temptation he steals 4 gallons of the mixture again, and fills it with water. When the liquid soap is checked at a station it isfound that the ratio of the liquid soap now left in the container to that of the water in it is 36 : 13. What was the initial amount of the liquid soap in the container if it is known that the liquid soap is neither used nor augmented by anybody else during the entire period?a)7 gallonsb)14 gallonsc)21 gallonsd)28 gallonsCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A thief steals four gallons of liquid soap kept in a train compartment’s bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection. Unable to resist the temptation he steals 4 gallons of the mixture again, and fills it with water. When the liquid soap is checked at a station it isfound that the ratio of the liquid soap now left in the container to that of the water in it is 36 : 13. What was the initial amount of the liquid soap in the container if it is known that the liquid soap is neither used nor augmented by anybody else during the entire period?a)7 gallonsb)14 gallonsc)21 gallonsd)28 gallonsCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thief steals four gallons of liquid soap kept in a train compartment’s bathroom from a container that is full of liquid soap. He then fills it with water to avoid detection. Unable to resist the temptation he steals 4 gallons of the mixture again, and fills it with water. When the liquid soap is checked at a station it isfound that the ratio of the liquid soap now left in the container to that of the water in it is 36 : 13. What was the initial amount of the liquid soap in the container if it is known that the liquid soap is neither used nor augmented by anybody else during the entire period?a)7 gallonsb)14 gallonsc)21 gallonsd)28 gallonsCorrect answer is option 'D'. Can you explain this answer?.
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