Divide ₹ 15,600 into two parts such that the interest on one at 5 percent for 5 years may be equal to that on the other at $4\dfrac{1}{2}$ per cent for 6 years.

Let the first part be ₹ $x$ and the second part be ₹ $(15,600 - x)$.

Hence

P₁ = ₹ $x$

R₁ = 5%

T₁ = 5 years

$\text{S.I.} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] \Rightarrow \text{S.I.} = \Big(\dfrac{x \times 5 \times 5}{100}\Big)\\[1em] \Rightarrow \text{S.I.} = \dfrac{25x}{100}\\[1em] \Rightarrow \text{S.I.} = \dfrac{x}{4}\\[1em]$

P₂ = ₹ $15,600 - x$

R₂ = $4\dfrac{1}{2}\%$

= $\dfrac{9}{2}\%$

T₂ = 6 years

$\text{S.I.} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] \Rightarrow \text{S.I.} = \Big[\dfrac{(15,600 - x) \times 9 \times 6}{2 \times 100}\Big]\\[1em] \Rightarrow \text{S.I.} = \dfrac{54(15,600 - x)}{200}\\[1em] \Rightarrow \text{S.I.} = \dfrac{27(15,600 - x)}{100}\\[1em]$

Both interest are equal.

$\dfrac{x}{4} = \dfrac{27(15,600 - x)}{100}\\[1em] \Rightarrow\dfrac{x}{4} = \dfrac{4,21,200 - 27x}{100}\\[1em] \Rightarrow\dfrac{x}{4} + \dfrac{27x}{100} = \dfrac{4,21,200}{100}\\[1em] \Rightarrow\dfrac{25x}{100} + \dfrac{27x}{100} = 4,212\\[1em] \Rightarrow\dfrac{(25x + 27x)}{100} = 4,212\\[1em] \Rightarrow\dfrac{52x}{100} = 4,212\\[1em] \Rightarrow x = \dfrac{4,212\times 100}{52}\\[1em] \Rightarrow x = \dfrac{4,21,200}{52}\\[1em] \Rightarrow x = 8,100$

Other amount will be ₹ (15,600 - 8,100) = ₹ 7,500.

Hence, ₹ 8,100 and ₹ 7,500 are the two parts.