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03 Jan 2021, 07:01
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A
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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
03 Jan 2021, 07:14
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Bunuel
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
General Discussion
\(1 : 2 : 4 (1+2+4=7)\) 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
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
