Two equal containers are filled with a mixture of water and petrol. One of them contains three times as much petrol as the other. The mixtures in the two containers are then mixed and it is found that the ratio of water to petrol is 3: 2. Find the ratio of water to petrol in each of the original containers.Choices:- 2:1, 3:4 1:3, 1:2 2: 3, 4: 1 None of the above
Question
Two equal containers are filled with a mixture of water and petrol. One of them contains three times as much petrol as the other. The mixtures in the two containers are then mixed and it is found that the ratio of water to petrol is 3: 2. Find the ratio of water to petrol in each of the original containers.Choices:- 2:1, 3:4 1:3, 1:2 2: 3, 4: 1 None of the above
Solution
Let's denote the volume of each container as V.
Let's denote the ratio of water to petrol in the first container as a:b and in the second container as c:d.
Given that the second container has three times as much petrol as the first, we can write the equation:
V * b = 3 * V * d
Solving for d, we get d = b/3.
Now, when the mixtures in the two containers are mixed together, the total volume is 2V and the ratio of water to petrol is 3:2.
So, we can write the equation:
(a + c) / (b + d) = 3 / 2
Substituting d = b/3 into the equation, we get:
(a + c) / (b + b/3) = 3 / 2
Solving for a + c, we get a + c = 9/5 * b.
Now, we can solve the system of equations for a, b, c, and d.
From the choices given, the only one that satisfies the equations is 2:1, 3:4.
So, the ratio of water to petrol in the first container is 2:1 and in the second container is 3:4.
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