The concentrations of three acids, A, B, and C, are specified as 20%, 30%, and 40%, respectively. They are blended in a ratio of 3 : 5 : a, yielding a solution with a concentration of 30%. What is the value of 'a'?

Question

Accepted Answer

Let the quantities of acids A, B, and C be 3x, 5x, and a·x respectively. Their concentrations are 20%, 30%, and 40%.

Total quantity = 3x + 5x + a·x = (8 + a)x

Total acid in mixture = (3x × 20%) + (5x × 30%) + (a·x × 40%)
= 3x × 0.2 + 5x × 0.3 + a·x × 0.4
= 0.6x + 1.5x + 0.4a·x
= (0.6 + 1.5 + 0.4a)x
= (2.1 + 0.4a)x

The final concentration is 30%, so:

(2.1 + 0.4a)x / (8 + a)x = 0.3

=> (2.1 + 0.4a) / (8 + a) = 0.3

=> 2.1 + 0.4a = 0.3(8 + a)
=> 2.1 + 0.4a = 2.4 + 0.3a
=> 0.4a - 0.3a = 2.4 - 2.1
=> 0.1a = 0.3
=> a = 0.3 / 0.1 = 3

Wait, this gives a = 3. Let's check the calculation step-by-step:

(2.1 + 0.4a) / (8 + a) = 0.3
=> 2.1 + 0.4a = 0.3(8 + a)
=> 2.1 + 0.4a = 2.4 + 0.3a
=> 0.4a - 0.3a = 2.4 - 2.1
=> 0.1a = 0.3
=> a = 3

But the correct answer is marked as 2 in the options. Let's check the options and the calculation again.

Given options:
1. 3
2. 1
3. 2
4. 4

From the calculation, a = 3. But the answer key says 2 is correct. Let's try with a = 2:

If a = 2:
Total quantity = 3 + 5 + 2 = 10
Total acid = 3 × 0.2 + 5 × 0.3 + 2 × 0.4 = 0.6 + 1.5 + 0.8 = 2.9
Concentration = 2.9 / 10 = 0.29 = 29%

If a = 3:
Total quantity = 3 + 5 + 3 = 11
Total acid = 3 × 0.2 + 5 × 0.3 + 3 × 0.4 = 0.6 + 1.5 + 1.2 = 3.3
Concentration = 3.3 / 11 = 0.3 = 30%

So, a = 3 is correct. The correct answer is option 1 (3).

Final answer: Option 1 (3) is correct.

Answer

Answer

Answer