Let the import in 2022 be I_2022 = ₹ 7200 cr. and export in 2022 be E_2022 = ₹ 6000 cr.In 2023, both figures are increased by 5%. I_2023 = I_2022 (1 + 5/100) = 7200 (1.05) E_2023 = E_2022 (1 + 5/100) = 6000 (1.05)In 2024, these figures are decreased by 5% (meaning from their 2023 values). I_2024 = I_2023 (1 - 5/100) = I_2023 (0.95) E_2024 = E_2023 (1 - 5/100) = E_2023 (0.95)Substitute the 1.05) 0.95We need to find the ratio of amount of import to export in 2024, which is I_2024 : E_2024. sides of the ratio. Ratio = 7200 : 6000This initial simplification is incorrect because the 5% decrease in 2024 is applied to the increased values of 2023. Let's calculate the actual values.Calculate I_2024: 756 0.5 = 378 I_2024 = 7560 - 378 = 7182Calculate E_2024: E_2023 = 6000 1.05 = 6300 E_2024 = 5985The ratio of import to export in 2024 is I_2024 : E_2024 = 7182 : 5985.Let's check the options: A) 7205 : 6005 (Incorrect) B) 6 : 5 (This is the ratio of 2022 values: 7200:6000 = 72:60 = 6:5. The percentages change this ratio) C) 7182 : 5985 (Correct) D) 7182 : 5982 (Incorrect)Alternatively, note that if a value is increased by x% and then decreased by x%, the final value is not the same as the original. (Original (1 + x/100)) (1 - x/100) = Original (1 - (x/100)²) So, I_2024 = 7200 (1 - E_2024 = 6000 (1 - (5/100)²) = 6000 (1 - 0.0025) = 6000 0.9975The ratio I_2024 : E_2024 = (7200 reasoning is incorrect because the question states "In 2023, these are increased by 5% but in 2024 the figures are decreased by 5%." This implies the 2024 decrease is applied to the 2023 figures, not cumulatively. The first method of calculating step-by-step is correct.Let's re-verify the interpretation: "In 2023, these are increased by 5%" - this means from 2022 to 2023. "but in 2024 the figures are decreased by 5%" - this means from 2023 to 2024. So my initial calculation was correct.I_2022 = 7200 E_2022 = 6000I_2023 = 7200 1.05 = 7560 E_2023 = 6000 6300 0.95 = 5985Ratio = 7182 : 5985.Let's simplify this ratio to see if it matches any other option, though C is directly the calculated value. Divide by 3: 7182 / 3 = 2394 5985 / 3 = 1995 Ratio = 2394 : 1995Divide by 3 again: 2394 / 3 = 798 1995 / 3 = 665 Ratio = 798 : 665Divide by 7: 798 / 7 = 114 665 / 7 = 95 Ratio = 114 : 95Divide by 19: 114 / 19 = 6 95 / 19 = 5 Ratio = 6 : 5Wait, this simplification is bringing me back to 6:5. This means the overall percentage change (increase by 5% then decrease by 5%) applied to both import and export results in the same ratio as the original values if the percentage changes are identical for both import and export.Let's check the phrasing again: "In 2023, these are increased by 5% but in 2024 the figures are decreased by 5%." This implies: Year 2022: I=7200, = 7200 : 6000 = 72 : 60 = 6 : 5.This is puzzling because option C is 7182 : 5985, and my step-by- step calculation yielded this. Let me re-check the calculation. I_2023 = 7200 1.05 = 7560 E_2023 = rect) E_2024 = 6300 0.95 = 5985 (Correct)The ratio is indeed 7182 : 5985. The simplification to 6:5 is correct if the question meant the overall change from 2022 to 2024 resulted in a net change, but the phrasing "In 2023..." and "in 2024..." suggests sequential changes.Let's review the interpretation of the percentage change. "In 2023, these are increased by 5%" => I_2023 = I_2022 1.05, E_2023 = E_2022 1.05 "but in 2024 the figures are decreased by 5%" => I_2024 = I_2023 0.95, E_2024 = E_2023 0.95This is what I calculated. So, I_2024 = common to both numerator and denominator of the ratio and can be cancelled out, leading to the ratio I_2022 : E_2022.Why is Option C (7182 : 5985) the correct answer? There must be a misinterpretation of the question or a mistake in the question itself/ options.Let's consider if the 5% decrease in 2024 was from the original 2022 figures instead of the 5700 Ratio = 6840 : 5700 = 684 : 570 = 342 : 285 = 114 : 95 = 6 : 5. Still 6:5.What if the increase by 5% was for 2023 and the decrease by 5% was also for 2023? That doesn't make sense.Let's assume the question meant: Year 2022: I=7200, E=6000 Year Year 2024: The figures (meaning the absolute values of import and export) were decreased by 5%. This phrasing is ambiguous. Does it mean the 2023 figures were decreased by 5% to get the 2024 figures? Or does it mean the import figures decreased by 5% and export figures decreased by 5% independently, but the decrease is not necessarily from the 2023 value?Let's go with the most direct interpretation: I_2022 = 7200, E_2022 = 6000 6300 I_2024 = 7560 0.95 = 7182 E_2024 = 6300 0.95 = 5985 Ratio = 7182 : 5985. This matches Option C.Now, why would this be the correct answer if mathematically it simplifies to 6:5? Perhaps the question setter wants the exact numerical ratio before simplification, or there's a context I'm missing where the specific values are important.Let's consider the possibility that the question implies different percentage changes. "In 2023, these are increased by 5%" (from 2022 to 2023 for both I and E). "but in 2024 the figures are decreased by 5%" (from 2023 to 2024 for both I and E).If I_2024 = 7182 and E_2024 = 5985, then the ratio is 7182 : 5985. This is directly option C. If the question implies a net change where the ratio should be the same as 2022 (6:5), then option B would be correct. However, since Option C is given as the correct answer, we must assume the step-by- step calculation of the values is what's required.Let's re-evaluate the simplification of 7182 :