Question

One container contains a mixture of spirit and water in the ratio 2: 3 and another contains the mixture of spirit and water in the ratio 3: 2. How much quantity from the second should be mixed with 10 litres of the first so that the resultant mixture has ratio of 4: 5? A) 2.86 litres B) 3.45 litres C) 4.31 litres D) 5.67 litres E) 8.94 litres


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Answer 1

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Answer 2

2.86 litres from the second should be mixed with 10 litres of the first so that the resultant mixture has a ratio of 4: 5.

Step-by-step explanation:

Step 1:

The ratio of the mixture of spirit and water in the first container = 2:3

So, we have  

The quantity of spirit from the 10 litres of the first container = $\frac{2}{2+3} * 10$ = 4 litres

And

The quantity of water from the 10 litres of the first container =  $\frac{3}{2+3} * 10$ = 6 litres

Step 2:

The ratio of the mixture of spirit and water in the second container = 3:2

Let’s say that “x” litres from the second container are mixed with the 10 litres of the first mixture.

So, we have  

The quantity of spirit from the x litres of the 2nd container = $\frac{3}{2+3} * x$ = (3/5)x litres

And

The quantity of water from the x litres of the 2nd container = $\frac{2}{2+3} * x$= (2/5)x litres

Step 3:

Now, according to the question, after mixing the 1st container with 2nd container, we can write the eq. as,

$\frac{4+\frac{3x}{5}}{6 + \frac{2x}{5} }  = \frac{4}{5}$

⇒ $\frac{20 + 3x}{30 + 2x}  = \frac{4}{5}$

⇒ 5 * [20 + 3x] = 4 * [30 + 2x]

⇒ 100 + 15x = 120 + 8x

⇒ 15x – 8x = 120 – 100

⇒ 7x = 20

⇒ x = 2.857 ≈ 2.86 litres

Thus, option (A): 2.86 litres of the mixture from the second container should be mixed with 10 litres of the first container.

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