77 Views

Question : In $t$ years, the simple interest earned on a certain amount at the rate of 10% per annum is $\frac{5}{8}$th of the principal amount. If the rate of interest is made three-fourths of 10% and the simple interest remains the same, which of the following statements is true about the changed value of time?

Option 1: It remains the same as $t$.

Option 2: It becomes three-fourths of the time $t$.

Option 3: It increases to $8 \frac{1}{3}$ years.

Option 4: It decreases to $5 \frac{1}{2}$ years.


Team Careers360 15th Jan, 2024
Answer (1)
Team Careers360 22nd Jan, 2024

Correct Answer: It increases to $8 \frac{1}{3}$ years.


Solution : Let the principal amount be $P$.
Simple interest after $t$ years at the rate of 10% per annum = $\frac{5}{8}P$
⇒ $\frac{P(10)t}{100}=\frac{5}{8}P$---(1)
⇒ $t=\frac{25}{4}$ years
New rate of interest $=\frac{3}{4}\times 10 = 7.5\%$
Let the new time taken for $P$ to become $\frac{5}{8}P$ at new rate of interest be $x$ years
⇒ $\frac{P(7.5)x}{100}=\frac{5}{8}P$---(2)
Dividing (1) and (2), we get,
$\frac{10t}{7.5x} = 1$
⇒ $x = \frac{4}{3}t$
⇒ $x=\frac{25}{3}$ years
⇒ $x=8\frac{1}{3}$ years
Hence, the correct answer is $8\frac{1}{3}$ years.

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