# Easy Percentages Solved QuestionAptitude Discussion

 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

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.

## (7) Comment(s)

Aman Sharma
()

nyc trick bro..givemore trick of short type

Zeeshan
()

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 + 16B3A=4BA:B = 4:3\$

Jessy
()

Yo bro, that's a cool way man.

Naaz
()

Thank you kartik, really very helpful :)

Sunny
()

3A=4B then ratio of A to B should be 3:4 isn't it KARTIK