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.
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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