Two vessels X and Y of capacities one and two litres respectively are completely filled with mixtures of two chemicals A and B. The ratio by volume of the chemicals A and B in X and Y are 3:2 and 4:5 respectively. The contents of A and B are mixed and the combination is kept in a vessel C of capacity of four litres. How many litres of Chemical A should be added to the combination so as to make the ratio of A to B equal to 1:1?Question 5Answera.1/270b.1/67c.1/68d.Not visible
Question
Two vessels X and Y of capacities one and two litres respectively are completely filled with mixtures of two chemicals A and B. The ratio by volume of the chemicals A and B in X and Y are 3:2 and 4:5 respectively. The contents of A and B are mixed and the combination is kept in a vessel C of capacity of four litres. How many litres of Chemical A should be added to the combination so as to make the ratio of A to B equal to 1:1?Question 5Answera.1/270b.1/67c.1/68d.Not visible
Solution
First, let's calculate the amount of chemical A and B in each vessel.
In vessel X (1 litre), the ratio of A to B is 3:2. So, the amount of A is 3/5 litre and B is 2/5 litre.
In vessel Y (2 litres), the ratio of A to B is 4:5. So, the amount of A is 4/9 litre and B is 5/9 litre.
When we mix the contents of X and Y in vessel C, the total amount of A is (3/5 + 4/9) litre and B is (2/5 + 5/9) litre.
To make the ratio of A to B equal to 1:1 in vessel C (4 litres), the amount of A and B should be equal.
Let's denote the amount of A that needs to be added as x. So, we have the equation:
(3/5 + 4/9 + x) = (2/5 + 5/9)
Solving this equation will give us the amount of A that needs to be added.
After solving, we get x = 1/45 litres.
So, 1/45 litres of chemical A should be added to the combination to make the ratio of A to B equal to 1:1.
Please note that this answer is not in the provided options (a.1/270, b.1/67, c.1/68, d.Not visible). There might be a mistake in the question or the options.
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