Two vessels have petrol, diesel and kerosene mixed in the ratio 2 : 3 : 5 and 2 : 4 : 3. If the quantities in the two vessels are mixed in the ratio 2 : 3, what is the ratio of petrol, diesel and kerosene in the resultant mixture?
Question
Two vessels have petrol, diesel and kerosene mixed in the ratio 2 : 3 : 5 and 2 : 4 : 3. If the quantities in the two vessels are mixed in the ratio 2 : 3, what is the ratio of petrol, diesel and kerosene in the resultant mixture?
Solution
To solve this problem, we need to find the quantity of each component (petrol, diesel, and kerosene) in the final mixture.
Step 1: Let's assume the quantity of the mixture in the first vessel is 2x and in the second vessel is 3x.
Step 2: In the first vessel, the ratio of petrol, diesel, and kerosene is 2:3:5. So, the quantities of petrol, diesel, and kerosene in the first vessel are 2/102x = 0.4x, 3/102x = 0.6x, and 5/10*2x = 1x respectively.
Step 3: In the second vessel, the ratio of petrol, diesel, and kerosene is 2:4:3. So, the quantities of petrol, diesel, and kerosene in the second vessel are 2/93x = 0.67x, 4/93x = 1.33x, and 3/9*3x = 1x respectively.
Step 4: When the two mixtures are combined, the quantities of petrol, diesel, and kerosene are added together. So, the quantities of petrol, diesel, and kerosene in the final mixture are 0.4x + 0.67x = 1.07x, 0.6x + 1.33x = 1.93x, and 1x + 1x = 2x respectively.
Step 5: The ratio of petrol, diesel, and kerosene in the final mixture is therefore 1.07x : 1.93x : 2x.
To simplify this ratio, we can divide each term by the smallest term, which is 1.07x. This gives us a final ratio of 1 : 1.8 : 1.87 approximately.
So, the ratio of petrol, diesel, and kerosene in the resultant mixture is approximately 1 : 1.8 : 1.87.
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