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kaushal

· started a discussion

· 1 Months ago

solution (Question: 78060.0 )

please send other short method for this....

Question:
A cane contains a mixture of two liquids 'A' and 'B' in the ratio 7 : 5. When 9 liters of mixture are drawn off and the cane is filled with 'B', the ratio of 'A' and 'B' becomes 7 : 9 liters. Liter of Liquid 'A' contained by the cane initially was?
Options:
A) 10 Liter
B) 20 Liter
C) 21 Liter
D) 25 Liter
Solution:

Initially, 

A = 7x litre, B = 5x litre (let)

 

In 9 litres of mixture,

A = \(\cfrac{7x}{12x}\) × 9 = \(\cfrac{21}{4}\) litre

B = \(\cfrac{5x}{12x}\) × 9 = \(\cfrac{15}{4}\) litre 

In new situation, 

\(\cfrac{7x-\cfrac{21}{4}}{5x-\cfrac{15}{4}+9}\)   = \(\cfrac{7}{9}\)

\(\Rightarrow\) \(\cfrac{28x-21}{20x-{15}+36}\)    = \(\cfrac{7}{9}\)

\(\Rightarrow\) 252x - 189 = 140x + 147

\(\Rightarrow\) 112x = 336

\(\Rightarrow\) x = 3

\(\therefore\) Initial quantity of liquid A

 = 7x = 7 × 3 = 21 litre

Talented Boy

· commented

· 1 Months ago

Let the total mixture be x litres.
So A will be (7x/12) lts.

After removing 9 lts, (7x9)/12 litres of A is gone.

So A will become (7x/12)-((7x9)/12).
Which is 7x/16 litres of the new mixture.

=>(7x/12)-((7x9)/12) = 7x/16.
=> 7(x-9)/12 = 7x/16.
=> (x-9)/3 = x/4.
=> 4x-36 = 3x.
=> x = 36 litres.

A in the original mixture = (7x36)/12 = 21 litres.
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