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Anynomus Kumari

· started a discussion

· 1 Months ago

x (Question: 104786.0 )

is there any shortcut

Question:
A bucket contains a mixture of two liquids A and B in the proportion 7: 5. If 9 liters of the mixture is replaced by 9 liters of liquid B, then the ratio of the two liquids becomes 7 : 9. How much of the liquid A was there in the bucket?
Options:
A) 21 liters
B) 23 liters
C) 25 liters
D) 27 liters
E) None of these
Solution:

Let the bucket contains liquid A and liquid B, 7x liters and 5x liters respectively.

After, taking 9 liters of mixture, the quantity of liquid

A in the bucket = 7x – 9 × \(\frac{7}{12}\) 

= 7x – \(\frac{63}{12}\)

and liquid B in the bucket, after replacing 9 liters mixture by 9 liters of liquid B.

= 12x -  \((7x-\frac{63}{12})\) = 5x + \(\frac{63}{12}\) 

According to question

 \(\frac{7x-\frac{63}{12}}{5x+\frac{63}{12}}\) = \(\frac{7}{9}\) 

⇒  \(\frac{12\times7x-63}{12\times5x+63}\) =  \(\frac{7}{9}\)

⇒ (84x – 63) × 9 = (60x+ 63) × 7

⇒ 84x × 9 - 60 x × 7 = 63 × 7 + 63 × 9

⇒ 336x = 63 × 16

x = \(\frac{63\times16}{336}\)  = 3

∴ Liquid A in bucket =7 × 3=21 liter.

Knowledge Expert

· commented

· 1 Months ago

7:5.
7:9.

7+5 = 12.
9-5 = 4.

9/12*4 = 3.
3*7 = 21.
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