The result of a number, when decreased by 66 2/3%, is 432. Find the number

Question

asked Jul 20, 2024 64.4k views

2 Answers

Andrii Radkevych · Answer 1 · 2024-07-26T09:23:40+0000

Answer:

1296

Explanation:

Let the unknown number be x.

If 432 is the result of x being decreased by 66²/₃%, then 432 is 33¹/₃% of x since 100% - 66²/₃% = 33¹/₃%.

Therefore:

$\implies 33(1)/(3)\%\;\textsf{of}\;x=432$

$\implies (33(1)/(3))/(100) \cdot x=432$

$\implies (33(1)/(3)x)/(100) =432$

Multiply both sides of the equation by 100:

$\implies 33(1)/(3)x =43200$

Rewrite 33¹/₃ as an improper fraction:

$\implies (100)/(3)x =43200$

Multiply both sides by 3:

$\implies 100x=129600$

Divide both sides by 100:

$\implies x=1296$

Therefore, the number that when decreased by 66²/₃% is 432, is 1296.