Question

90% and 97% pure acid solutiins are mixed to obtain 21 lit of 95% pure acid sol. Find the quantity of each type of acid to be mixed

Answer 1

A helpful formula for questions like x litres of a% solution, y litres of b% solution are mixed to get z litres of a c% solution -

$ax + by = cz$

Applying this to our question,

$90x + 97y = 95 \times 21$

Where x and y are quantity of first and second solution respectively

We also know that x + y = 21

So x = 21 - y

Use this in the equation

$90(21 - y) + 97y = 95 \times 21$

So

$90 \times 21 - 90y + 97y = 95 \times 21$

So

$1890 - 90y + 97y = 95 \times 21$

$1890 + 7y = 95 \times 21$

$1890 + 7y = 1995$

Transpose

$7y = 1995 - 1890$

$7y = 105$

Divide both sides by 7

$y = 15$

Use this in x + y =21

$x = 6$

Therefore, you need 6 litres of 90% solution and 15 litres of 97% solution

Hope this helps

Answer 2

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.

★ HOPE IT WILL HELP YOU ★

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