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A number whose fifth part increase by 4 is equal to its fourth part diminished by 10, is :
Answer & Solution
Correct Answer:
Option
D
Let the number be x
Then,
$$\eqalign{ & \Leftrightarrow \frac{x}{5} + 4 = \frac{x}{4} - 10 \cr & \Leftrightarrow \frac{x}{4} - \frac{x}{5} = 14 \cr & \Leftrightarrow \frac{x}{{20}} = 14 \cr & \Leftrightarrow x = 14 \times 20 \cr & \Leftrightarrow x = 280 \cr} $$
Then,
$$\eqalign{ & \Leftrightarrow \frac{x}{5} + 4 = \frac{x}{4} - 10 \cr & \Leftrightarrow \frac{x}{4} - \frac{x}{5} = 14 \cr & \Leftrightarrow \frac{x}{{20}} = 14 \cr & \Leftrightarrow x = 14 \times 20 \cr & \Leftrightarrow x = 280 \cr} $$
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