A chemist has two solutions. One is 50% acidic and another is 25% acidic. To make 10 L of 40% acidic solution, how much of each should be combined?

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6 L and 4 L

5 L and 5 L

3 L and 7 L

2 L and 8 L

answer is A.

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Detailed Solution

It is given that a chemist has two solutions, one is 50% acidic and another is 25% acidic and he needs to make 10 L of 40% acidic solution.
Let the amount of the first solution needed to make the 10 L solution is

x

and the amount of the second solution needed is

y .

Since both the solutions are combined to make 10 L of solution.

∴ x + y = 10 ⇒ y = 10 − x (1)

It is given that one solution is 50% acidic and another is 25% acidic. Therefore we have,

0.5 x + 0.25 y = 0.4 (10) ⇒ 50 x + 25 y = 400 ⇒ 2 x + y = 16

⇒ 2 x + (10 − x) = 16, using eq (1) ⇒ x = 16 − 10 ⇒ x = 6

Therefore from equation (1), we have,

y = 10 − x ⇒ y = 10 − 6 ⇒ y = 4

Thus, to make 10 L of 40% acidic solution, we need 6 L of the first solution and 4 L of the second solution to be combined.
Hence option (1) is correct.

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