Answer:
Let the unknown number be x. 1/4th if x is x/4 and 2/3rd of x is 2x/3. Then according to the question,
2x3−5=x4
⟹2x3−x4=5
⟹8x−3x12=5
⟹5x12=5
⟹x=12×55=12
Thus the number is 12.
The number which when multiplied by [tex]\frac{1}{4}[/tex] is 50 less than when it is
multiplied by [tex]\frac{2}{3}[/tex] is 120.
Let x represent the number, expressing as fractions, we have;
[tex]x \times \dfrac{1}{4}= \mathbf{x \times \dfrac{2}{3} - 50}[/tex]
Which gives;
[tex]\mathbf{x \times \dfrac{1}{4} + 50} = x \times \dfrac{2}{3}[/tex]
[tex]50 = x \times \dfrac{2}{3} - x \times \dfrac{1}{4} = x \times \dfrac{5}{12}[/tex]
[tex]x = 50 \times \dfrac{12}{5} = 120[/tex]
Therefore;
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