Ratios & Proportion
Aptitude

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Q.

If $40\%$ of a number is equal to two-third of another number, what is the ratio of first number to the second number?

 A.

$2:5$

 B.

$3:7$

 C.

$7:3$

 D.

$5:3$

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Solution:
Option(D) is correct

let $40\%$  of A = \(\dfrac{2}{3}\)

Then \(\dfrac{40A}{100}=\dfrac{2B}{3}\)

\(\begin{align*} \Rightarrow \dfrac{2A}{5}=\dfrac{2B}{3}\\ \Rightarrow A:B=5:3 \end{align*}\)

Edit: Thank you, Anurag, corrected the typo.

Edit 2: Thank you Sanju Sharma, corrected the typo.

Edit 3: For an alternative solution, check comment by Sikandar Naeem.


(6) Comment(s)


Sikandar Naeem
 ()

Suppose two numbers are $4$ & $y$

$40\%$ of $x$ is equal to $2/3$ of $y$

$\dfrac{40}{100} x = \dfrac{2}{3} y$

$\dfrac{2}{5} x= \dfrac{2}{3} y$

$\dfrac{x}{y} = \dfrac{2}{3} * \dfrac{5}{2}$

$\dfrac{x}{y} = \dfrac{10}{6}$

$\therefore \dfrac{x}{y} = \dfrac{5}{3}$

Now changing fraction into ratio,

$x : y = 5 : 3$



Sanju Sharma
 ()

You wrote 5 instead of 3 in given solution.

$a \times \dfrac{2}{5}=b \times \dfrac{2}{3}$


Deepak
 ()

Thank you, corrected it.


Anurag
 ()

I think the question needs to be modified. Instead of 40 of a number, it should be 40 percent of a number.


Deepak
 ()

Thank you for letting me know, corrected the typo.


Raji
 ()

Huh I'm confused.. it's 1/5:1/3.

IF A is smaller than B then so is its ratio