Question

Two solutions of 90% and 97% purity were mixed, resulting in 42 litres of mixture of
94% purity. How much is the quantity of the first solution in the resulting mixture?​

Answer 1

Answer:

Method 1 to solve the equation.

Let us assume the number of liters of the 90% purity solution = A

and the number of liters of the 97% purity solution = B.

According to question,

Since there are 21 liters of the solution,

A + B = 21 ...................... (1)

Since after mixing the two solutions the new mixture has 94% purity,

Concentrate of A + Concentrate of B = Concentrate of (A + B)

A x 90% + B x 94% = (A+ B) x 97%

⇒ A x 90/100 + B x 97/100 = (A + B) x 94/100

⇒ 90A + 97B = (A + B) x 94

⇒ 90A + 97B = 94A + 94B

⇒ 94A + 94B - 90A- 97B = 0

⇒ 4A - 3B = 0 ........................(2)

Multiply the 3 with Equation (1) and add with Equation (2),

3A + 3B + 4A - 3B = 63 + 0

⇒ 7A = 63

⇒ A = 63/7 = 9

Put the value of A in Equation (1) , we will get

9 + B = 21

B = 21 - 9

B = 12

The first solution would be A = 9 liters.

Method 2 to solve the equation.

Hit and trail method.

94% is closer to 97% but barely meaning the mixtures will not be equal parts but will be slightly more of the higher purity. Quickly eliminate A and B. Out of the others 9 is the easy choice. If the other choices were closer to half this wouldn't work.

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Step-by-step explanation: