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A vessel of capacity 126 litre is full of water. If 9 litre of the water is taken out and replaced by the same amount of spirit and further 7 litre of the mixture is taken out and replaced by the same amount of spirit then find the amount of spirit in the mixture at the end of the 2nd process (in litre)?
  • a)
    15.5
  • b)
    15
  • c)
    14.5
  • d)
    14
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A vessel of capacity 126 litre is full of water. If 9 litre of the wat...
Given:
Capacity of vessel = 126 litre
Amount of water taken out and replaced with spirit = 9 litre
Amount of mixture taken out and replaced with spirit = 7 litre

To find:
Amount of spirit in the mixture at the end of the 2nd process

Solution:

Step 1: Amount of water in the vessel initially
As the vessel is full of water,
Amount of water = 126 litre

Step 2: Amount of water in the vessel after 1st replacement
As 9 litre of water is taken out and replaced with spirit,
Amount of water = 126 - 9 = 117 litre
Amount of spirit = 9 litre

Step 3: Amount of mixture in the vessel after 2nd replacement
As 7 litre of mixture is taken out and replaced with spirit,
Amount of mixture = 117 - 7 = 110 litre

Let x be the amount of spirit in the mixture after 2nd replacement.
Then, the amount of water in the mixture = 110 - x

Step 4: Applying alligation method

Amount of Spirit | Amount of Water | Total
--------------- | -------------- | -----
9 | 117 | 126
x | 110 - x | 110

Using alligation method,

(117 - x)/(x + 9) = 7/9

9(117 - x) = 7(x + 9)

1053 - 9x = 7x + 63

16x = 990

x = 61.875

Therefore, the amount of spirit in the mixture at the end of the 2nd process = 61.875 ≈ 15.5 litre

Hence, the correct option is (A) 15.5.
Free Test
Community Answer
A vessel of capacity 126 litre is full of water. If 9 litre of the wat...
Initially water is 126 ltrs, out of which 9ltrs water is removed and replaced by spirit, now
water = 126-9= 117 ltrs
spirit = 9 ltrs
ratio of Water : Spirit = 117: 9 = 13:1 ( Total mixture is 13+1= 14parts)
water is (13/14 parts) and spirit is (1/14) parts.
Now 7 ltrs mixture is removed i.e,
Water = 117-(13/14)*7 = 117- (13/2) = 221/2
Spirit = 9- (1/14)*7 = 9-(1/2)= 17/2
Again same quantity (7ltrs) of spirit is replaced
Spirit= (17/2)+7 = 31/2 = 15.5 ltrs..

Cross check by solving quantities of water and spirit and add both quantities
water = 221/5 = 110.5
spirit = 31/2 = 15.5
Water + Spirit = 110.5+15.5= 126 ltrs...
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A vessel of capacity 126 litre is full of water. If 9 litre of the water is taken out and replaced by the same amount of spirit and further 7 litre of the mixture is taken out and replaced by the same amount of spirit then find the amount of spirit in the mixture at the end of the 2nd process (in litre)?a)15.5b)15c)14.5d)14Correct answer is option 'A'. Can you explain this answer?
Question Description
A vessel of capacity 126 litre is full of water. If 9 litre of the water is taken out and replaced by the same amount of spirit and further 7 litre of the mixture is taken out and replaced by the same amount of spirit then find the amount of spirit in the mixture at the end of the 2nd process (in litre)?a)15.5b)15c)14.5d)14Correct answer is option 'A'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A vessel of capacity 126 litre is full of water. If 9 litre of the water is taken out and replaced by the same amount of spirit and further 7 litre of the mixture is taken out and replaced by the same amount of spirit then find the amount of spirit in the mixture at the end of the 2nd process (in litre)?a)15.5b)15c)14.5d)14Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vessel of capacity 126 litre is full of water. If 9 litre of the water is taken out and replaced by the same amount of spirit and further 7 litre of the mixture is taken out and replaced by the same amount of spirit then find the amount of spirit in the mixture at the end of the 2nd process (in litre)?a)15.5b)15c)14.5d)14Correct answer is option 'A'. Can you explain this answer?.
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