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'?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 3.
The amount of A in the solution is 20g in 100g of water,
The amount of B in the solution is 30g in 100g of water,
The amount of C in the solution is 40g in 100g of water.
After mixing
The amount of A in the solution is 20 × 3g = 60 g in 100 × 3 g = 300 g of water,
The amount of B in the solution is 30 × 5g = 150 g in 100 × 5 g = 500 g of water,
The amount of C in the solution is 40 × a g = 40x g in 100 × a g = 100a g of water.
So, the final solution contains (60 + 150 + 40a)g = (210 + 40a)g of the given
substances in (300 + 500 + 100a)g = (800 + 100a)g of water.
So, the concentration, which is 30% is,
⇒ (210 + 40a)/(800 + 100a) = 30/100
⇒ 10(210 + 40a) = 3(800 + 100a)
⇒ 2100 + 400a = 2400 + 300ax
⇒ 100a = 300
⇒ a = 3
Thus, the value of a is 3