The ratio of the prices of first two fans was 16 : 23. Two years later, when the price of the first fan had risen by 10% and that of the second by ₹ 477, the ratio of their prices became 11 : 20. Find the original prices of the two fans.

Let price of first fan be f₁ and second fan be f₂.

Given,

Ratio of the prices of first two fans was 16 : 23.

$\Rightarrow \dfrac{f$1}{f2} = \dfrac{16}{23} \\[1em] \Rightarrow f1 = \dfrac{16f2}{23} ……….(1)

First fan price after 2 years = $f$1 + \dfrac{10}{100}f1 = f1 + \dfrac{f1}{10} = \dfrac{11f_1}{10}.

Second fan price after two years = $f_2 + 477$.

Given,

Ratio of fan's prices becomes 11 : 20 after 2 years.

$\therefore \dfrac{\dfrac{11}{10}f$1}{f2 + 477} = \dfrac{11}{20} \\[1em] \Rightarrow \dfrac{11f1}{10(f2 + 477)} = \dfrac{11}{20} \\[1em] \Rightarrow \dfrac{f1}{f2 + 477} = \dfrac{11}{20} \times \dfrac{10}{11} \\[1em] \Rightarrow \dfrac{f1}{f2 + 477} = \dfrac{1}{2} \\[1em] \Rightarrow f1 = \dfrac{f2 + 477}{2}

Substituting value of f₁ from (1) in above equation we get :

$\Rightarrow \dfrac{16f$2}{23} = \dfrac{f2 + 477}{2} \\[1em] \Rightarrow 16f2 \times 2 = 23(f2 + 477) \\[1em] \Rightarrow 32f2 = 23f2 + 10971 \\[1em] \Rightarrow 32f2 - 23f2 = 10971 \\[1em] \Rightarrow 9f2 = 10971 \\[1em] \Rightarrow f2 = \dfrac{10971}{9} \\[1em] \Rightarrow f_2 = 1219.

Substituting value of f₂ in equation (1), we get :

$\Rightarrow f$1 = \dfrac{16f2}{23} \\[1em] = \dfrac{16 \times 1219}{23} \\[1em] = 16 \times 53 \\[1em] = 848.

Hence, original price of fans are ₹ 848 and ₹ 1219.