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Two vessels A and B contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively. Find the ratio in which these mixture be mixed to obtain a new mixture in vessel C containing spirit and water in the ration 8 : 5 ?
  • a)
    3: 4
  • b)
    4 : 3
  • c)
    9 : 7
  • d)
    7 : 9
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Two vessels A and B contain spirit and water in the ratio 5 : 2 and 7 ...
Spirit in 1 litre mix of A = 5/7 litre.
Spirit in 1 litre mix of B = 7/13 litre.
Spirit in 1 litre mix of C = 8/13 litre. 
By rule of alligation we have required ratio X:Y

   X         :       Y

 5/7              7/13

 

       \          /
          (8/13)

       /          \


(1/13)     :     (9/91)

  7                      9

Therefore required ratio = 1/13 : 9/91 

= 7:9
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Most Upvoted Answer
Two vessels A and B contain spirit and water in the ratio 5 : 2 and 7 ...
Given information:
- Vessel A contains spirit and water in the ratio 5 : 2
- Vessel B contains spirit and water in the ratio 7 : 6
- Vessel C should contain spirit and water in the ratio 8 : 5

To find: Ratio in which A and B should be mixed to obtain the desired ratio in C

Solution:
Let's assume that A and B are mixed in the ratio x : y, where x represents the quantity of A and y represents the quantity of B.

From the given information, we can write the following equations:
- For vessel A: Spirit:Water = 5:2 => Spirit = (5/7)*(spirit+water), Water = (2/7)*(spirit+water)
- For vessel B: Spirit:Water = 7:6 => Spirit = (7/13)*(spirit+water), Water = (6/13)*(spirit+water)
- For vessel C: Spirit:Water = 8:5 => Spirit = (8/13)*(spirit+water), Water = (5/13)*(spirit+water)

Now, we can write the following equation based on the quantity of spirit in each vessel:
x*(5/7) + y*(7/13) = (x+y)*(8/13)

Solving this equation, we get:
x/y = 7/9

Therefore, A and B should be mixed in the ratio 7 : 9 to obtain the desired ratio in C.

Answer: Option D (7 : 9)
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Community Answer
Two vessels A and B contain spirit and water in the ratio 5 : 2 and 7 ...
By alligation- 5/7 7/13 / 8/13 / 1/13 9/91 ie 7:9
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Two vessels A and B contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively. Find the ratio in which these mixture be mixed to obtain a new mixture in vessel C containing spirit and water in the ration 8 : 5 ?a)3: 4b)4 : 3c)9 : 7d)7 : 9Correct answer is option 'D'. Can you explain this answer?
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