Ratio and Proportion

Concept:Represent the original prices using a common factor $x$, apply the given changes, and equate the resulting ratio to find $x$.Explanation:Let the original prices be $16x$ and $23x$.After two years, the first car's price increases by 10%, so its new price is $1.1 \times 16x = 17.6x$.The second car's price increases by Rs. 477, so its new price is $23x + 477$.The new ratio is $11 : 20$, which gives the equation:$\frac{17.6x}{23x + 477} = \frac{11}{20}$.Cross‑multiply: $20 \times 17.6x = 11(23x + 477)$.Compute: $352x = 253x + 5247$.Simplify: $352x - 253x = 5247 \implies 99x = 5247 \implies x = 53$.Original price of first car = $16 \times 53 = 848$ Rs.Original price of second car = $23 \times 53 = 1219$ Rs.Answer:The original prices are Rs. 848 and Rs. 1219, which matches option A.