18 litres of Petrol was added to a vessel containing 80 litres of Kero...
Answer – E. None of the Above Explanation : Total quantity of the mixture = 18+80 = 98 litre quantity of petrol remaining = 18/2 = 9 quantity of kerosene remaining = 80/2 = 40 (40 + 2x) / (9 + x) = 4 / 1 x = 2 Quantity of kerosene added in the vessel = 2x = 4 litre
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18 litres of Petrol was added to a vessel containing 80 litres of Kero...
Given:
Initial quantity of petrol = 18 litres
Initial quantity of kerosene = 80 litres
Quantity of mixture taken out = 49 litres
Let's solve this problem step by step.
Step 1: Finding the quantity of petrol and kerosene in the vessel after adding 18 litres of petrol
Total quantity of petrol = Initial quantity of petrol + Added petrol = 18 litres + 18 litres = 36 litres
Total quantity of kerosene = Initial quantity of kerosene = 80 litres
Step 2: Finding the quantity of petrol and kerosene in the mixture taken out
Let's assume x litres of petrol and y litres of kerosene were present in the mixture taken out.
According to the given information, the ratio of kerosene and petrol in the mixture taken out is 4:1.
So, we have the equation:
y/x = 4/1
Also, the total quantity of mixture taken out is 49 litres.
So, we have another equation:
x + y = 49
Solving these two equations, we get:
x = 7 litres
y = 28 litres
Step 3: Finding the quantity of petrol and kerosene in the vessel after adding more petrol and kerosene in the ratio 2:1
Let's assume a litres of petrol and b litres of kerosene were added to the vessel.
According to the given information, the ratio of kerosene and petrol added is 2:1.
So, we have the equation:
b/a = 2/1
Also, the total quantity of petrol and kerosene in the vessel after adding is:
Total quantity of petrol = Initial quantity of petrol + Added petrol = 36 litres + a litres
Total quantity of kerosene = Initial quantity of kerosene + Added kerosene = 80 litres + b litres
Step 4: Finding the quantity of kerosene added in the vessel
Now, we need to find the value of b (quantity of kerosene added to the vessel).
To find b, we can use the equation y/x = 4/1 from Step 2.
Substituting the values of y and x from Step 2, we get:
28/a = 4/1
Cross-multiplying, we get:
4a = 28
a = 7
Substituting the value of a in the equation b/a = 2/1 from Step 3, we get:
b/7 = 2/1
Cross-multiplying, we get:
b = 14
Therefore, the quantity of kerosene added in the vessel is 14 litres.
Hence, the correct answer is option E) None of the above.