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

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Solution

The correct option is B 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 $20 \times 3 g = 60 g$ in $100 \times 3 g = 300 g$ of water,
the amount of B in the solution is $30 \times 5 g = 150 g$ in $100 \times 5 g = 500 g$ of water,
the amount of C in the solution is $40 \times x g = 40 x g$ in $100 \times x g = 100 x g$ 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,
$\frac{210 + 40 x}{800 + 100 x} = \frac{30}{100} ⟹ 2100 + 400 x = 2400 + 300 x ⟹ 100 x = 300 ⟹ x = 3.$
Ans- Option C

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