Quantitative Aptitude – Algebra – Polynomial Equations – The product of two positive numbers is 616
Slot – 1 – Quantitative Aptitude – Algebra – Polynomial Equations – The product of two positive numbers is 616
The product of two positive numbers is 616 – Video
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?
85
50
95
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