90% pure and 97% pure acid solutions are mixed to obtain 21 litres of 95% pure acid solutions. find the quantity of each type of acid to be mixed to form the mixture
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Answer:
\huge {\mathcal{\purple{H}\green{e}\pink{y}\blue{!}}}Hey!
Let the given solutions be A and B respectively.
Let X litres of A be mixed with Y litres of B .
Then,
X + Y = 21 ---------(1)
★Quantity of acid in X litres of A = (90% of X ) Litres
=> ( 90/100 × X ) Litres
=> 9X / 10 Litres
★ Quantity of acid in Y litres of B = (97% of Y ) litres
=> ( 97/100 × Y ) Litres
=> (97Y/100) litres
★ Quantity of acid in 21 litres of (A + B) = ( 95% of 21 litres )
=> ( 95/100 × 25) litres
=> ( 399/20 ) litres
Therefore,
9X / 10 + 97Y/100 = 399/20
=> 90X + 97Y = 1995 --------(2)
Multiply equation (1) by 90 we get,
90X + 90Y = 1890 -----------(3)
Subtract equation (3) from equation (2) we get,
90X + 97Y = 1995
90X + 90Y = 1890
----------------------------
7Y = 105.
Y = 105/7 = 15
Putting the value of Y in equation (1)
X + Y = 21
X + 15 = 21
X = 21-15
X = 6
So,
6 litres of 90% solution is mixed with 15 litres of 97% solution.
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