Question

Concentrations of three solutions A, B and C are 20%, 30% and 40% respectively. They are mixed in the ratio 3 : 5 : x resulting in a solution of 30% concentration. Find x. 

(a) 5

(b) 2

(c) 3

(d) 4

Answer 1

Correct option is (c) 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 = 60g in 100 × 3g = 300g of water,

the amount of B in the solution is 30 × 5g = 150g in 100 × 5g = 500g of water,

the amount of C in the solution is 40 × xg = 40xg in 100 × xg = 100xg of water.

So the final solution contains (60 + 150 + 40x)g = (210 + 40x)g  of the given substances in (300 + 500 + 100x)g = (800 + 100x)g of water.

So the concentration, which is 30% is,

\(\frac{210 +40x}{800 + 100x} = \frac{30}{100}\)

⇒ 2100 + 400x = 2400 + 300x

⇒ 100x = 300

⇒ x = 3.