Two vessels contain a mixture of Spirit and water. In the first

Question

Two vessels contain a mixture of Spirit and water. In the first vessel the ratio of Spirt to water is 8 : 3 and in the second vessel the ratio is 5 : 1. A 35 litre cask is filled from these vessels so as to contain a mixture of Spirit and water in the ratio of 4 : 1. How many litres are taken from the first vessels ?

(A) 11 litres
(B) 16.5 litres
(C) 22 litres
(D) 27.5 litres
(E) none of these

Show Answer

Official Answer

A

(A) 11 litres
(B) 16.5 litres
(C) 22 litres
(D) 27.5 litres
(E) none of these

Babineaux · Accepted Answer

Please go through the pic uploaded.

IMO ans is A

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v12345 · Answer

Ratio--------------Spirit-------Water-------Total
1st vessel-----------8------------3-----------11
2nd vessel----------5------------1------------6
Final-----------------4------------1------------5

Converting these ratios to same total, 
Ratio--------------Spirit-------Water-------Total
1st vessel----------240---------90---------330
2nd vessel---------275---------55---------330
Final--------------- 264---------66---------330

Now, final ratios of two solutions will be 
1st vessel : 2nd vessel
(275 - 264) : (264 - 240)
=> 11 : 24

As final solution is 35 litre, first solution will be  \frac{11}{(11+24)} * 35  = 11 litre

Hence answer (A)

Kudos, if you liked the solution

effatara · Answer

Let us assume that the quantity taken from the 1st solution (S1) is 11x liters of which Water is 3x liters. Then the qty taken from S2 is (35-11x) liters of which Water is (35-11x)/6 liters.
The qty of water in the final 35 liter solution is thus {3x+(35-11x)/6} which must be equal to (1/5)*35=7.
3x+(35-11x)/6=7...> 18x+35-11x=42...> x=1. T/4, quantity taken from S1 is 11*1=11 liters.

ANS: A

vtexcelgmat · Answer

I tried to prepare a table initially, but it did not turn out as I visualized.

For better representation of solution, refer to attached Image.
I know that the Image lacks explanation but seasoned test-takers may understand nevertheless.
Hit  Like  if you understood.

yashikaaggarwal · Answer

Let the solution in container A = 8x:3x (where 8x is spirit and 3x is water)
the solution in container B = 5y:1y (where 5y is spirit and 1y is water)
THE NEW VESSEL OF 35 LITRES CAPACITY,
It contains 4:1 ratio of spirit and water. 
That means 28litre spirit and 7 litre water.

Therefore,
8x+5y = 28 ----------(1)
3x+y = 07 ----------(2)
Multiply second equation with 5
Therefore,
 8x+5y = 28 
15x+5y = 35
Equating both 
X = 1

So the quantity taken first vessel = 8x+3x = 8+3 = 11

Answer is A

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jcerdae · Answer

Hi!
Why 330 in the total??

jcerdae · Answer

Hi!
Thank you for the solution! it is super easy to understand! (Kudos guaranteed) 
Could you tell me what is the name of the approach or where can I see more of this ??

For example: do I always have to subtract after multiplying? (5/6 - 4/5 & 4/5 - 8/11)
or depends in the case?

And how did you get the 11:24?

Thank you!!

Babineaux · Answer

jcerdae This is called Alligation method. An easy way to approach such problems. The highlighted part is not multiplication. Please refer the video link, it will help you understand. https://youtu.be/4jHnQjw7Ji4

MathRevolution · Answer

Ratio --------- Spirit ---------- Water -------- Total

First vessel  --------- 8 ---------------- 3 --------------- 11 (8+3)
 Second vessel  --------- 5 ---------------- 1 --------------- 6 (5+1)
 Final vessel  --------- 4 ---------------- 1 --------------- 5 (5)

The total values are 11,6,5. Take LCM of 11, 6, and 5 which is 330 to make the total value common for all the vessels.

Ratio ---------- Spirit --------- Water ---------- Total

First vessel  --------- 240 ------------- 90 --------------- 330 (11*30)
 Second vessel  ---------275 -------------- 55 --------------- 6 (6*55)
 Final vessel  --------- 264 -------------- 66 --------------- 5 (5 * 66)

Final ratio ---> (Second - Final) : (Final - 1st vessel)  (Rule of alligation)

=> (275 - 264) : (264-240)
=> 11 : 24

Final solution => 35 litres

=>  \frac{11 }{ (11+24) } * 35 = 11 litres

Answer A

Thelionking1234 · Answer

Can you explain me this step? Why you have added 11 and 24 in denominator?

Babineaux · Answer

Thelionking1234 ,

First you have to understand,

11 : 24 is the ratio between the solution from first vessel and the solution from second vessel.

Now, As 11 + 24 = 35, the total mixture contains  \frac{11}{35}  of first vessel (11 parts out of 35),  \frac{24}{35}  of second vessel.

Now as the cask contains 35 liters of solution, so the amount from first vessel is  \frac{11}{35}  x 35 = 11 liters.

For your conceptual clarification, say the cask contains 105 liters of solution,

So the amount from the first vessel must be,  \frac{11}{35}  x 105 = 11 x 3 = 33 liters.

And the amount from the second vessel must be,  \frac{24}{35}  x 105 = 24 x 3 = 72 liters.

If you add these two amounts 33 + 72 you will ultimately get 105 liters.

Hope you understand.

malikvce · Answer

An alloy contains 24% of tin by weight. How much more tin to the nearest kg must be added to 100 kg of the alloy so that the % of tin may be doubled?
please solve this one with this technique

Crytiocanalyst · Answer

let the first vessel be in the ratio 8x +3x 
and the second vessel be 5y + y

ther ratio being =4/1 = 8x+5y / 3x +y 
y= 4x ............1

and 11x + 6y = 35 
x=1 from .......1

Therefore total litres from vessel1 = 11 liters

Therefore IMO A

Sabby · Answer

Hi,

First of all, let's break down this problem:
we have vessel A which has a ratio of Spirit to Water of 8a:3a
and we have vessel B which has a ratio of Spirit to Water of 5b:1b

Now, we fill these two vessel into a vessel of 35 liters with a ratio of Spirit to Water of 4c:1c which equals 5c. Therefore 5c=35 and c=7. We can obtain the amount of liters for the spirit which equals 28 liters and for the water which equals 7 liters.

Hence, 28 liters = 8a+5b and 7 liters = 3a+1b
Let's take 7 liters = 3a+1b ==> it means that either a= 2 and b=1 or a=1 and b=4

Let's test a=2 and b=1 : 28=8a+5b=16+5 =21 this is not possible 21 
Now let's test a=1 and b=4 : 28=8a+5b= 8+20=28 this is a match!

We can conclude that a=1 and b=4 and that 11 liters come from vessel A (8a+3a= 11a and as a=1 11(1)=11)

ALGEBRAIC APPROACH

8a+5b=28
3a+b=7
b=7-3a

Therefore 8a+5(7-3a) = 28
8a+35-15a=28
7=7a
a=1

b=7-3a=7-3(1)= 4

8a:3a=11a= 11

Answer A

Mugdho · Answer

Sprit : Water
 8 : 3
 5 : 1

In 35L of the cask 28L is sprit and 7L is water.

Let first vessel has X Liter
 second vessel has Y Liter

So, ATQ,
 (8X+5Y)/(3X+1Y)=28/7
 =>X/Y=1/4

So, Final Ratio => Sprit:Ratio
 8*1 : 3:1
 and 5*4 : 1*4

So,(8+3)=11L of the first vessel and (20+4)=24L of the second vessel will make 35 L.

So answer is 11L.

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KevoK · Answer

I think I have a "kinda" different approach compared to most responses (sorry if I'm wrong, there are too many responses so I just skimmed some of them) so I wanna chime in.

From the information provided, we know that:
in 11 Liter of mixture A, 8L will be Spirit, 3L will be water
in 6 Liter of Mixture B, 5L will be spirit, 1L will be water
Instead of solving, I just test the answer instead:

the final casket has 35 liter in 4:1 Spirit - water ratio, so there would be  28L of Spirit in total and 7L Water  in total. Our mission is to test the correct amount from casket 1.

By testing A first, we have 11 liter from A and the remaining 35 - 11 = 24 Liter from B

11 Liter from A so there will be  8L Spirit, 3L of water

24 Liter from B, so there will be  5*4 = 20L Spirit, 1*4= 4 L of water

Summing the ratio, we can see that it is  28L of Spirit in total and 7L Water , the ratio we want

So  A

Two vessels contain a mixture of Spirit and water. In the first

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Two vessels contain a mixture of Spirit and water. In the first

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