How can we calculate a profit share for Rs. 100,000 that remained in an account for 5 days only. See this question illustration below
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The simple approach is if you consider simple interest, not compound. The Rs $10,000$ represents $300,000$ Rs-days of deposit. The Rs $100,000$ represents $500,000$ Rs-days of deposit. So the $100,000$ should get $\frac 5{5+3}=\frac 58$ of the profit, ofr $\frac 58 \cdot 2500=1562.5$ As the duration is short and the profit is small compared to the amount, compounding will not matter much, as you can see from the other answer.
Let $B_{\rm{in}}=10,000, R_s=100,000, B_{\rm{fin}}=B_{\rm{in}}=10,000,P=2,500$. Let $\pi(R_s)$ the profit share of $R_s$. Calling $i$ the compound monthly interest rate, you have to find $i$ such that $$ B_{\rm{in}}(1+i)+\underbrace{R_s(1+i)^{5/30}-R_s}_{\pi(R_s)}=B_{\rm{in}}+P $$ Solving numerically, you'll find $i\approx 9.6\%$. So the profit share of $R_s$ for 5 days is $$\pi(R_s)=R_s(1+i)^{5/30}-R_s\approx 1,539.81$$
Note that the profit share of $B_{\rm{in}}$ is $$\pi(B_{\rm{in}})=B_{\rm{in}}(1+i)-B_{\rm{in}}\approx 960.19$$ and the total profit is $P=\pi(B_{\rm{in}})+\pi(R_s)=2,500$.
If the bank use the simple interest rate $j$, then you have to find $j$ such that $$ B_{\rm{in}}(1+j)+\underbrace{R_s\left(1+j\frac{5}{30}\right)-R_s}_{\pi(R_s)}=B_{\rm{in}}+P $$ that is $$j=\frac{P}{B_{\rm{in}}+\frac{R_s}{6}}\approx 9.38\%$$ and $\pi(B_{\rm{in}})\approx 937.50$ and $\pi(R_s)\approx 1,562.50$.