Question 103
Find the value expression $$\left(750\left(\frac{x^2 + y^2}{xy}\right)\right)$$, where ₹x is the amount when a sum of ₹y is lent at an unknow interest rate for an unknow period compounded quaterly. Also ₹y is the amount when a sum of ₹9x is lent under similar condition as above.
Solution
We will assume the interest rate = 4r% pa and the time period to be t years.
$$X\ =\ Y\left(1+r\right)^{4t}$$.
And $$Y=\ 9X\left(1+r\right)^{4t}$$.
Equating value of $$\left(1+r\right)^{4t}$$ from both the equations to get:
$$\frac{X}{Y}=\frac{Y}{9X}$$.
$$Y^2\ =\ 9X^2$$ ==> Y = 3X.
After putting this into the equation, we get: $$750\times\ \left(\frac{9X^2+X^2}{3X^2}\right)=2500$$.
