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Mathematics

90% acid solution (90% pure acid and 10% water) and 97% acid solution are mixed to obtain 21 litres of 95% acid solution. How many litres of each solution are mixed.

Linear Equations

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Answer

Let x litres of 90% and y litres of 97% be mixed; then

⇒ x + y = 21

⇒ x = 21 - y …….(1)

and

⇒ 90% of x + 97% of y = 95% of 21

⇒90100x+97100y=95100×21⇒90x+97y=95×21⇒90x+97y=1995 ……..(2)\Rightarrow \dfrac{90}{100}x + \dfrac{97}{100}y = \dfrac{95}{100} \times 21 \\[1em] \Rightarrow 90x + 97y = 95 \times 21 \\[1em] \Rightarrow 90x + 97y = 1995 \text{ ……..(2)}

Substituting value of x from equation (1) in equation (2), we get :

⇒ 90(21 - y) + 97y = 1995

⇒ 1890 - 90y + 97y = 1995

⇒ 7y = 1995 - 1890

⇒ 7y = 105

⇒ y = 1057\dfrac{105}{7} = 15.

Substituting value of y in equation (1), we get :

⇒ x = 21 - 15 = 6.

Hence, 6 litres of 90% acid solution and 15 litres of 97% of acid solution are mixed.

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