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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
- e)4 : 7 : 12
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Two vessels have petrol, diesel and kerosene mixed in the ratio 1 : 2 ...
To solve this problem, we need to find the ratio of petrol, diesel, and kerosene in the resultant mixture when the quantities from two vessels are mixed in a 1:1 ratio.
Let's assume that the quantities in the first vessel are x, 2x, and 4x respectively for petrol, diesel, and kerosene. Similarly, let's assume that the quantities in the second vessel are y, 5y, and 6y respectively for petrol, diesel, and kerosene.
We are given that the two vessels are mixed in a 1:1 ratio. So, the total quantity of petrol in the mixture is x + y, the total quantity of diesel is 2x + 5y, and the total quantity of kerosene is 4x + 6y.
Now, we need to find the ratio of petrol, diesel, and kerosene in the resultant mixture. Let's assume that the ratio is a:b:c. Therefore, we have:
(x + y)/(2x + 5y) = a/b
(x + y)/(4x + 6y) = a/c
Cross-multiplying these equations, we get:
b(x + y) = a(2x + 5y)
c(x + y) = a(4x + 6y)
Expanding these equations, we get:
bx + by = 2ax + 5ay
cx + cy = 4ax + 6ay
Rearranging the terms, we get:
2ax - bx = 5ay - by
4ax - cx = 6ay - cy
Factoring out the common terms, we get:
x(2a - b) = y(5a - b)
x(4a - c) = y(6a - c)
Since x and y are non-zero, we can cancel them out from both equations. This gives us:
2a - b = 5a - b
4a - c = 6a - c
Simplifying these equations, we get:
a = 1
0 = 0
Since a = 1, we can substitute this value into the equations to find the values of b and c:
2(1) - b = 5(1) - b
4(1) - c = 6(1) - c
Simplifying these equations, we get:
2 - b = 5 - b
4 - c = 6 - c
Since the left-hand side and right-hand side are equal in both equations, we can conclude that b and c can be any value.
Therefore, the ratio of petrol, diesel, and kerosene in the resultant mixture is 1:b:c, which simplifies to 1:2:4.
Hence, the correct answer is option A: 1:2:4.
Let's assume that the quantities in the first vessel are x, 2x, and 4x respectively for petrol, diesel, and kerosene. Similarly, let's assume that the quantities in the second vessel are y, 5y, and 6y respectively for petrol, diesel, and kerosene.
We are given that the two vessels are mixed in a 1:1 ratio. So, the total quantity of petrol in the mixture is x + y, the total quantity of diesel is 2x + 5y, and the total quantity of kerosene is 4x + 6y.
Now, we need to find the ratio of petrol, diesel, and kerosene in the resultant mixture. Let's assume that the ratio is a:b:c. Therefore, we have:
(x + y)/(2x + 5y) = a/b
(x + y)/(4x + 6y) = a/c
Cross-multiplying these equations, we get:
b(x + y) = a(2x + 5y)
c(x + y) = a(4x + 6y)
Expanding these equations, we get:
bx + by = 2ax + 5ay
cx + cy = 4ax + 6ay
Rearranging the terms, we get:
2ax - bx = 5ay - by
4ax - cx = 6ay - cy
Factoring out the common terms, we get:
x(2a - b) = y(5a - b)
x(4a - c) = y(6a - c)
Since x and y are non-zero, we can cancel them out from both equations. This gives us:
2a - b = 5a - b
4a - c = 6a - c
Simplifying these equations, we get:
a = 1
0 = 0
Since a = 1, we can substitute this value into the equations to find the values of b and c:
2(1) - b = 5(1) - b
4(1) - c = 6(1) - c
Simplifying these equations, we get:
2 - b = 5 - b
4 - c = 6 - c
Since the left-hand side and right-hand side are equal in both equations, we can conclude that b and c can be any value.
Therefore, the ratio of petrol, diesel, and kerosene in the resultant mixture is 1:b:c, which simplifies to 1:2:4.
Hence, the correct answer is option A: 1:2:4.
Community Answer
Two vessels have petrol, diesel and kerosene mixed in the ratio 1 : 2 ...
To ensure an equal quantity of mixture, we aim to find equivalent ratios with equal sums of their terms. The original ratios are 1:2:4 and 3:5:6.
By multiplying all terms of the first ratio by 2, we obtain the equivalent ratio of 2:4:8. Notably, the sum of these terms is 14. Therefore, in 14 units of the first mixture, there are 2 units of petrol, 4 units of diesel, and 8 units of kerosene.
Similarly, in 14 units of the second mixture, we have 3 units of petrol, 5 units of diesel, and 6 units of kerosene.
When combining 14 units of each mixture, we end up with a total of 28 units. These units can be expressed in the ratio (2+3):(4+5):(8+6), which simplifies to 5:9:14.
Therefore, the correct answer is option A, 5:9:14.
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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 : 14b)3 : 6 : 8c)4 : 8 : 11d)4 : 7 : 10e)4 : 7 : 12Correct answer is option 'A'. Can you explain this answer?
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