Divide ₹ 10,800 into two parts so that if one part is put at 18% per annum S.I. and the other part is put at 20% p.a. S.I. the total annual interest is ₹ 2,060.

Let the first part be ₹ $x$ and the second part be ₹ $(10,800 - x)$.

Hence

P₁ = ₹ $x$

R₁ = 18%

T₁ = 1 year

$\text{S.I.} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] = \Big(\dfrac{x \times 18 \times 1}{100}\Big)\\[1em] = \dfrac{18x}{100}\\[1em] = \dfrac{9x}{50}\\[1em]$

P₂ = ₹ $10,800 - x$

R₂ = $20\%$

T₂ = 1 year

$\text{S.I.} = \Big[\dfrac{P \times R \times T}{100}\Big]\\[1em] = \Big[\dfrac{(10,800 - x) \times 20 \times 1}{100}\Big]\\[1em] = \dfrac{20(10,800 - x)}{100}\\[1em] = \dfrac{(10,800 - x)}{5}\\[1em]$

Total amount = ₹ 2,060

$\Rightarrow \dfrac{9x}{50} + \dfrac{(10,800 - x)}{5} = 2,060\\[1em] \Rightarrow \dfrac{9x}{50} + \dfrac{10(10,800 - x)}{50} = 2,060\\[1em] \Rightarrow \dfrac{9x}{50} + \dfrac{(1,08,000 - 10x)}{50} = 2,060\\[1em] \Rightarrow \dfrac{(9x + 1,08,000 - 10x)}{50} = 2,060\\[1em] \Rightarrow 1,08,000 - x = 2,060 \times 50\\[1em] \Rightarrow 1,08,000 - x = 1,03,000\\[1em] \Rightarrow x = 1,08,000 - 1,03,000\\[1em] \Rightarrow x = 5,000\\[1em]$

Other part = ₹ 10,800 - ₹ 5,000

= ₹ 5,800

Hence, the two parts are ₹ 5,000 at 18% and ₹ 5,800 at 20%.