The one-fifth part of a number when raised by 5 equals its one-fourth part decreased by 5. What is the number?

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300

250

350

200

answer is D.

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Detailed Solution

Given, the one-fifth part of a number when raised by 5 equals to its one-fourth part decreased by 5.
Let the required number be x.
According to the question,

\frac{x}{5} + 5 = \frac{x}{4} - 5

.
Solve the equation for x.

\frac{x}{5} + 5 = \frac{x}{4} - 5

\frac{x}{4} - \frac{x}{5} = 10

The prime factorisation of 4 is

2 \times 2

.
The prime factorisation of 5 is 5.
So, the LCM between 4 and 5 is 20.

\frac{5 x - 4 x}{20} = 10

\frac{x}{20} = 10

x = 200
So, the number is 200.
Hence, option 4 is correct.

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