Two vessels have petrol, diesel and kerosene mixed in the ratio 1 : 2

Question

Two vessels have petrol, diesel and kerosene mixed in the ratio 1 : 2 : 4 and 3 : 5 : 6. If the quantities in the two vessels are mixed in the ratio 1 : 1, what is the ratio of petrol, diesel and kerosene in the resultant mixture?

(A) 5 : 9 : 14
(B) 3 : 6 : 8
(C) 4 : 8 : 11
(D) 4 : 7 : 10
(D) 4 : 7 : 12

(A) 5 : 9 : 14 
(B) 3 : 6 : 8 
(C) 4 : 8 : 11 
(D) 4 : 7 : 10
(D) 4 : 7 : 12

BrentGMATPrepNow · Accepted Answer

In order to find equal quantities to be mixed, we'll need to find equivalent ratios such that the SUMS of the terms are equal. 
 1 + 2 + 4 =  7   
 3 + 5 + 6 =  14

Take the ratio  1 : 2 : 4  and multiply all terms by  2  to get the equivalent ratio:  2 : 4 : 8 
Notice that  2 + 4 + 8 =  14  
So, in   14   units of the first mixture, there are  2  units of petrol,  4  units of diesel and  8  units of kerosene.
Similarly,   14   units of the second mixture, there are  3  units of petrol,  5  units of diesel and  6  units of kerosene.

When we combine  14  units of each mixture, we get 28 units in the ratio: ( 2  +  3 ) : ( 4  +  5 ) : ( 8  +  6 ), which simplifies to be  5 : 9 : 14

Answer: A

imeanup · Answer

1 : 2 : 4 (1+2+4=7)  and  3 : 5 : 6 (3+5+6=14)

Multiply  2  with the first ratio to make the  1_{st}  mixture equal to  2_{nd}  mixture.
The new ratio for the  1_{st}  mixture is  2:4:8

Combining an equal proportion  1:1  in the final mixture. So, the new ratio is;
 2+3:4+5:8+6=5:9:14

Ans A

rocky620 · Answer

LCM of 1,2,3,4,5,6 = 60

Lets assume that we mix 60L of each mixture.

Mixture1 
p:d:k = 1:2:4

p=60/7
d=120/7
k=280/7

Mixture1 
p:d:k = 3:5:6

p=90/7
d=150/7
k=180/7

Mix1+Mix2

p=(60+90)/7 = 150/7
d=(120+150)/7 = 270/7
k=(240+180/7 = 420/7

Final ratio = 150:270:420 =  5:9:14

Option A

Abulikabuli · Answer

Let give a clearer explanation.
Vessel 1: p:d:k = x:2x:4x or total 7x units.
Vessel 2; 3y:5y:6y or total 14y units.
Now these two are mixed in 1:1 or equal proportions, as in 7x=14y or x=2y
So vessel 1 p:d:k is 2y:4y:8y and vessel 2 is 3y:5y:6y
Mix them and in new vessel p;d;k is 5y:9y:14y. BINGO!  Ans: (A)

btsaami · Answer

Use alligation,

If we consider the qty of kerosene, in the mixture of ratio 1:1, we have

8/14-----7/14-----6/14

That means the kerosene is half the qty in the mixture. Sum of petrol and diesel is equal to qty of kerosene.
We can check from each option that only A satisfies. Hence A

btsaami · Answer

Let both the solutions be 70 ltrs each mixed in ratio 1:1.
So we have, Ratio of P: D: K in first solution= 10:20:40
Similarly, for solution, we get 15:25:30

Adding both, we get 25:45:70 or 5:9:14

iocharidwar · Answer

1:2:4 = 1/7: 2/7:4/7
3:5:6= 3/14:5/14:6/14

Petrol = 1/7+3/14 = 5/14
Diesel = 2/7 + 5/14 = 9/14
Kerosene = 4/7 + 6/14 = 14/14

Petrol : diesel : kerosene = 5:9:14

luisdicampo · Answer

Deconstructing the Question

Vessel I ratio:
 1 : 2 : 4

Vessel II ratio:
 3 : 5 : 6

The two vessels are mixed in the ratio  1 : 1 , meaning equal quantities.

So we compute each component per unit and then add.

Step-by-step

Total parts in vessel I:

1+2+4=7

So per 1 unit:

\frac{1}{7}, \frac{2}{7}, \frac{4}{7}

Total parts in vessel II:

3+5+6=14

So per 1 unit:

\frac{3}{14}, \frac{5}{14}, \frac{6}{14}

Add corresponding components:

Petrol:

\frac{1}{7} + \frac{3}{14} = \frac{2}{14} + \frac{3}{14} = \frac{5}{14}

Diesel:

\frac{2}{7} + \frac{5}{14} = \frac{4}{14} + \frac{5}{14} = \frac{9}{14}

Kerosene:

\frac{4}{7} + \frac{6}{14} = \frac{8}{14} + \frac{6}{14} = \frac{14}{14}

Multiply ratio by 14:

5 : 9 : 14

Answer: A

Two vessels have petrol, diesel and kerosene mixed in the ratio 1 : 2

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Two vessels have petrol, diesel and kerosene mixed in the ratio 1 : 2

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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