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Q.

Two numbers $A$ and $B$ are such that the sum of 5% of $A$ and 4% of $B$ is two-third of the sum of 6% of $A$ and 8% of $B$.

Find the ratio of $A : B.$

 A.

2 : 3

 B.

1 : 1

 C.

3 : 4

 D.

4 : 3

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Solution:
Option(D) is correct

$5\% \text{ of } A + 4\% \text{ of } B = \dfrac{2}{3}(6\% \text{ of } A + 8\% \text{ of } B)$

$\Rightarrow \left(\dfrac{5}{100}\right)×A + \left(\dfrac{4}{100}\right)×B = \dfrac{2}{3}\left(\dfrac{6}{100}×A + \dfrac{8}{100}×B\right)$
$\Rightarrow \left(\dfrac{1}{20}\right)×A + \left(\dfrac{1}{25}\right)×B = \left(\dfrac{1}{25}\right)×A + \left(\dfrac{4}{75}\right)×B$
$\Rightarrow \left(\dfrac{1}{2} - \dfrac{1}{25}\right)×A = \left(\dfrac{4}{75} - \dfrac{1}{25}\right)×B$
$\Rightarrow \left(\dfrac{1}{100}\right)×A = \left(\dfrac{1}{75}\right)×B $
$\Rightarrow \dfrac{A}{B} = \dfrac{100}{75} = \dfrac{4}{3}$

So required ratio = 4:3

Edit: For easier calculation, check out KARTIK's observation.


(6) Comment(s)


Aman Sharma
 ()

nyc trick bro..givemore trick of short type



Zeeshan
 ()

Karthic ur answer is 3:4 (answer c)


ABHIJEET
 ()

zeeshan.. his name is kartik not karthick


KARTIK
 ()

you could cancel off the % on both side by taking \dfrac{1}{100}$ common. that way it would be easy to solve the equation.

$5A+4B=(2/3)(6A+8B)$

$15A+12B = 12A + 16B$

$3A=4B$

$A:B = 4:3$


Jessy
 ()

Yo bro, that's a cool way man.

Naaz
 ()

Thank you kartik, really very helpful :)