44 Views

Question : Five years from now, the ratio of the ages of A, B and C will be 3 : 5 : 2. The sum of the squares of their present ages is 525. What is the present age of B?

Option 1: 10 years

Option 2: 15 years

Option 3: 25 years

Option 4: 20 years


Team Careers360 9th Jan, 2024
Answer (1)
Team Careers360 14th Jan, 2024

Correct Answer: 20 years


Solution : The ratio of ages of A, B and C after 5 years = 3 : 5 : 2
Let the ages of A, B and C after 5 years be $3x, 5x$ and $2x$ respectively.
Present ages of A, B and C = $(3x-5), (5x-5), (2x-5)$
The sum of squares of present ages = 525
So, $(3x-5)^2 + (5x-5)^2 + (2x-5)^2 = 525$
$⇒9x^2 - 30x + 25 + 25x^2 - 50x + 25 + 4x^2 - 20x + 25 = 525$
$⇒38x^2 - 100x + 75 = 525$
$⇒38x^2 - 100x - 450 = 0$
$⇒38x^2 - 190x + 90x - 450 = 0$
$⇒38x(x-5) + 90(x-5) = 0$
$⇒(38x + 90)(x-5) = 0$
Since age cannot be negative,
$x = 5$
Present age of B = $5x - 5= 5 × 5 - 5= 25 - 5= 20$
Hence, the correct answer is 20 years.

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