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

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

300

250

350

200

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th