There are two vessels A & B. Vessel A contains 80L mixture of petrol

Question

There are two vessels A & B. Vessel A contains 80L mixture of petrol and kerosene oil in the ratio of 7 : 3 and Vessel B contains petrol and kerosene oil in the ratio 5 : 9. 20L mixture of vessel A is poured into Vessel B, due to which ratio of petrol and kerosene oil in vessel B becomes 11 : 15. Then, find the initial quantity of mixture in vessel B.

(A) 72 liters
(B) 78 liters
(C) 84 liters
(D) 90 liters
(E) 96 liters

Why doesn't this yield the correct ans?

x= Initial volume of B

14+(5x/14)=(11/26)*(20+x)

(A) 72 liters
(B) 78 liters
(C) 84 liters
(D) 90 liters
(E) 96 liters

chetan2u · Answer

20l mixture of petrol and kerosene oil in the ratio of 7 : 3 means 14l of petrol and 6l of kerosene.
Vessel B contains petrol and kerosene oil in the ratio 5 : 9 or 5x:9x..Total = 14x

When you mix the two the new ratio is 11:15, so petrol is 11/26 of the total, 20+14x, which should also be equal to sum of individual quantity of petrol, 14+5x
=>  14+5x=\frac{11}{11+15 }*(20+14x) 
 26(14+5x)=11(20+14x).....364+130x=220+154x......24x=144....x=6 
Total = 14x=14*6=84

CrackverbalGMAT · Answer

Here the information that vessel A contains 80 L is not important

20 L from vessel A, will contain (7/10) * 20 = 14 L of petrol and 20 - 14 = 6 L of kerosene

Let there be x L in Vessel B. 
Initial Amount of petrol = (5/14) * x
Initial Amount of kerosene = (9/14) * x

Final amount of petrol = 5x/14 + 14
Final amount of kerosene = 9x/14 + 6

This ratio is 11:15
Therefore (5x/14 + 14) / (9x/14 + 6) = 11/15
5x + 196 / 9x + 84 = 11/15
15(5x + 196) = 11(9x + 84)
75x + 2940 = 99x + 924

99x - 75x = 2940 - 924
24x = 2016
x = 2016/24 = 84 L

Option C

Arun Kumar

satya2029 · Answer

For A
20 litres contains 7/10*20
=14 litres petrol + 6 litres of kerosene
When it mixed with B
ratio becomes=11/15
11/15= 5x+14/9x+6
x=6
Initial quantity of B 5x+9x=14X
=14*6
=84
C:)

vtexcelgmat · Answer

Let me share a simple method. NO NEED FOR COMPLEX MULTIPLICATIONS/ DIVISIONS/ ADDITIONS/ SUBTRACTIONS. This question is too simple for these.

If one looks at the options, one can find that all are Integers. This is an IMPORTANT WEAKNESS in the question. If exploited in a smart way, it will crack open the problem in seconds.
Initially, the ratio was  5:9  , this means the quantity should be  a multiple of 14 .
 HOW? 
Suppose Petrol is  5X  litres and Kerosene is  9X  litres = Total  14X  Litres.
Remember all options are Integers? Thus, the quantity should be a multiple of  14 .

Moreover,  X  should be a integer greater that 5 (may be 6 or 7 or 8 ).  WHY?  (See the options, most of them are slightly greater than 70.)

Now, How many options are multiple of 14 ? Leave 14 – How many are multiples of 7 ?
Only 84. That’s your Answer.
Hit it and move ahead to next one!!!!

sdas80923 · Answer

Why doesn't this yield the correct ans?

x= Initial volume of B

14+(5x/14)=(11/26)*(20+x)

Bunuel · Answer

Your equation is actually correct and give x = 84, which is option C.

SSPatil · Answer

IDK is it good to use this approach or not (because luck is involved) but I just simply added the ratios of B i.e. 5+9=14. 
Inferred that the initial value should be divisible by 14 and luckily there was only one value which is 84 so my answer is C.

There are two vessels A & B. Vessel A contains 80L mixture of petrol

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There are two vessels A & B. Vessel A contains 80L mixture of petrol

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