8 Views

Question : The difference between the compound interest (compounding half-yearly) for 1 year and the simple interest for 1 year on a certain sum lent out at the annual rate of 10% is Rs, 25. What is the sum?

Option 1: Rs. 12000

Option 2: Rs. 6000

Option 3: Rs. 8000

Option 4: Rs. 10000


Team Careers360 17th Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

Correct Answer: Rs. 10000


Solution : Given,
Difference between compound interest and simple interest = Rs. 25,
Annual interest rate = 10%
We know,
Compound Interest for 1 year = $P[(1 + \frac{r}{100})^n- 1]$, where $r$ is the annual interest rate and $n$ is the number of compounding periods.
Simple Interest for 1 year = $\frac{P × r × t}{100}$, where $r$ is the annual interest rate and $t$ is the time in years.
Let the principal sum be $P$.
The given difference is:
⇒ $P[(1 + \frac{5}{100})^2 - 1] - \frac{P × 10 × 1}{100} = 25$
⇒ $P[(1+0.05)^2-1]-\frac{P}{10}=25$
⇒ $P[(1.05)^2-1]-\frac{P}{10}=25$
⇒ $P[1.1025-1]-0.1P=25$
⇒ $0.1025P-0.1P=25$
⇒ $0.0025P=25$
⇒ $P = \text{Rs.}\ 10000$
Hence, the correct answer is Rs. 10000.

How to crack SSC CHSL

Candidates can download this e-book to give a boost to thier preparation.

Download Now

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books