Quantitative Aptitude – Algebra – Equation


Slot – 1 – Quantitative Aptitude – Algebra – Equation – The product of two positive numbers is 616

Q. The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157:3, then the sum of the two numbers is?
  1. 85
  2. 50
  3. 95
  4. 58
Answer: 50

Solution: Let the number be a and b.
So ab = 616
Given, (a^3 –b^3)/(a-b)^3 = 157/3
(a-b)*(a^2 + b^2 +ab)/(a-b)*(a^2 + b^2 -2ab) = 157/3
Let a^2 + b^2 =k
So (k+ab)/(k-2ab) = 157/3
3k + 3ab = 157k – 314ab
154k = 117ab = 317*616
k = 317*616/154 = 1268
As we know (a+b)^2 = (a^2 + b^2) + 2ab = k + 2ab = 1268 + 2*616
(a+b)^2 =2500 = 50^2
So a+b = 50

Online Coaching Course for CAT 2020

a) 900+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video