28 Views

Question : If the sum of two numbers is 60 and their HCF and LCM are 5 and 60, respectively, then the sum of the reciprocals of the numbers will be:

Option 1: $\frac{1}{11}$

Option 2: $\frac{1}{6}$

Option 3: $\frac{1}{4}$

Option 4: $\frac{1}{5}$


Team Careers360 6th Jan, 2024
Answer (1)
Team Careers360 22nd Jan, 2024

Correct Answer: $\frac{1}{5}$


Solution : Let the two numbers be $x$ and $y$.
The sum of two numbers = 60
⇒ $x+y=60$
HCF of the given numbers = 5
LCM of the given numbers = 60
We know that,
Product of two numbers = LCM × HCF
⇒ $xy$ = LCM × HCF
⇒ $xy$ = 5 × 60
The required sum = $\frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}$
Putting the values, we get:
= $\frac{60}{5 × 60}$
= $\frac{1}{5}$
Hence, the correct answer is $\frac{1}{5}$.

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