Acid mixture

Logic Level 3

90% and 97% pure acid solutions are mixed to obtain 21 litres of 95% pure acid solution. Find the quantity of 90% type of acid to form the mixture.

6 litres 17 litres 15 litres 12 litres 7 litres

Vilakshan Gupta by Vilakshan Gupta , 19, India

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2 solutions

Chew-Seong Cheong
Jul 17, 2017

Let the volumes of 90% and 97% pure acid used in the mixture be V a V_a an V b V_b litres, so that V a + V b = 21 V_a+V_b=21 . Then we have:

0.9 V a + 0.97 V b = 0.95 ( V a + V b ) 0.9 V a + 0.97 ( 21 − V a ) = 0.95 ( 21 ) ( 0.97 − 0.9 ) V a = 21 ( 0.97 − 0.95 ) 0.07 V a = 21 ( 0.02 ) V a = 6 litres \begin{aligned} 0.9V_a + 0.97 V_b & = 0.95 (V_a+V_b) \\ 0.9V_a + 0.97(21-V_a) & = 0.95 (21) \\ (0.97-0.9)V_a & = 21(0.97-0.95) \\ 0.07 V_a & = 21(0.02) \\ V_a & = \boxed{\text{6 litres}} \end{aligned}

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There is typo in 3rd step.It's 0.95, not 0,95. :)

genis dude - 3 years, 10 months ago

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Thanks, amended.

Chew-Seong Cheong - 3 years, 10 months ago
Genis Dude
Aug 14, 2017

Using allegation method will give the answer in less than a minute.

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