A number whose one fifth part is increased by 4 is equal to its one fourth part diminished by 16, then the number is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 400
Write the two descriptions of the same quantity as expressions and set them equal. Let the number be \(x\):
One fifth increased by 4 equals one fourth diminished by 16: \(\displaystyle\frac{x}{5}+4=\frac{x}{4}-16\)
\(\displaystyle\frac{x}{4}-\frac{x}{5}=20\)
A fourth of a number minus a fifth of it is one twentieth of it: \(\displaystyle\frac{x}{20}=20\)
\(x=400\)