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himanshu singh

· started a discussion

· 1 Months ago

SHORT TRICK (Question: 78060.0 )

INITIAL RATIO 7:5=12
FINAL RATIO 7:9=16
KYUNKI TOTAL MIX SAME HI ISLIYE 12 AUR 16 KO BALANCE KARIYE
MATLAB LCM(12,16)=48
YA FIRST RATIO 28:20=48 AUR SECOND RATIO 21:27=48 HO GYA
AB A MIX MEIN JO KAMI AAYI HI WO NIKALNE KI WAJAH SE AAYI HI
JO 28 SE 21 HO GYA HI YANI KI MIX A MEIN SE 7 NIKLA HI.
TO TOTAL MIXTURE 7:5=12MIX NIKALA GYA THO JO KI 9LTR DIYA HI AUR A KI INITIAL VALUE PUNCH RHA H JO 28 HI.
MEANS 12=9LITER THEN 28=(28*9)/12=21LITER ANS

PRACTISE KARNE PE 2 LINE MEIN ANS AA JAYEGA

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

Knowledge Expert

· commented

· 1 Months ago

Dear Student,
You can definitely use the short trick.
We have provided general approach.

Thanks and Regards
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