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- Two solution of 90% and 97% purity and mixed resulting in 21 liters of mixture of 94% purity.
Question 1:
Two solution of 90% and 97% purity and mixed resulting in 21 liters of mixture of 94% purity.How much is the quantity of the first solution in the resulting mixture?
A. 15 litres
B. 12 litres
C. 9 litres
Feedback 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.
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.
D. 6 litres
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