correct answer is: d) ₹ 2700 & ₹ 900

Explanation

Let, One part is ₹ x
\therefore Other part is ₹\left(3600\;-\;x\right)
Here,
One part ‘P’ =₹ x & other part ‘P’ =₹\left(3600\;-\;x\right)
One part ‘R’ = 9 % & other part ‘R’ = 10 %
T = 1 year _[both]
We know, S.I. =\frac{p\times r\times t}{100}
According to the question,
\left(\frac{x\times9\times1}{100}\right)+\{\frac{\left(3600\ -\ x\right)\times10\times1}{100}\} = ₹ 333
\rightarrow\frac{9x}{100}+\frac{\left(3600\ -\ 10x\right)}{100} = ₹ 333
\rightarrow\ \frac{9x\ +\left(36000\ -\ 10x\right)}{100} = ₹ 333
\rightarrow\ 9x+36000-10x=₹ 33300 _{[cross multiply]}
\rightarrow\left(-x+36000\right)= ₹ 33300
\rightarrow\ -x=₹\left(33300-36000\right)
\rightarrow\ x = ₹ 2700
\therefore One part is ₹ x or ₹ 2700 .
Other part is ₹\left(3600\;-\;x\right) or ₹\left(3600\;-\;2700\right) or ₹ 900
Ans: One part is ₹ 2700 & Other part is ₹ 900 .

Another way to ask this same question is:
1. How to divide ₹3600 to achieve ₹333 annual income with 9% and 10% interest rates?
2. What is the strategy to split ₹3600 into two parts for ₹333 total annual income?
3. Dividing ₹3600 into two parts with 9% and 10% interest – how to reach ₹333 annually?
4. Solving for ₹333 annual income: How to split ₹3600 with 9% and 10% interest?
5. What division of ₹3600 yields ₹333 in annual income with 9% and 10% interest?