Aptitude Discussion

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. |
$5:3$ |

**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.**

**Sikandar Naeem**

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**Sanju Sharma**

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You wrote 5 instead of 3 in given solution.

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

Thank you, corrected it.

**Anurag**

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

Thank you for letting me know, corrected the typo.

**Raji**

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

IF A is smaller than B then so is its ratio

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,

$x : y = 5 : 3$