What is the ratio of the number of people of age group-I of city A and D…

Concept: When a total is split in the ratio a : b : c, every part is the total multiplied by its own share over the sum of all the shares, so the first group holds total × a/(a + b + c). To compare two aggregates that are each built this way, compute every part from its own total and its own ratio, add the parts within each aggregate, and reduce the resulting comparison to its lowest terms.

Application: Each city carries its own population and its own age-group ratio, so the share formula is applied city by city before anything is added.

1. City A: population 14.4 lakh with age-group ratio I : II : III = 1 : 3 : 2, so the shares sum to 1 + 3 + 2 = 6. Age-group-I people = 14.4 × 1/6 = 2.4 lakh.

2. City D: population 12.8 lakh with ratio 3 : 1 : 4, so the shares sum to 3 + 1 + 4 = 8. Age-group-I people = 12.8 × 3/8 = 4.8 lakh.

3. Cities A and D together therefore hold 2.4 + 4.8 = 7.2 lakh age-group-I people.

4. City C: population 19.2 lakh with ratio 1 : 1 : 2, so the shares sum to 1 + 1 + 2 = 4. Age-group-I people = 19.2 × 1/4 = 4.8 lakh.

5. City E: population 12 lakh with ratio 1 : 3 : 1, so the shares sum to 1 + 3 + 1 = 5. Age-group-I people = 12 × 1/5 = 2.4 lakh.

6. Cities C and E together therefore hold 4.8 + 2.4 = 7.2 lakh age-group-I people.

7. Required comparison = 7.2 : 7.2, and dividing both sides by 7.2 reduces it to 1 : 1.

Cross-check: Setting the four age-group-I counts side by side shows where the equality comes from.

The two pairs are built from the same two counts, 2.4 lakh and 4.8 lakh, simply exchanged between them: A supplies 2.4 and D supplies 4.8, while C supplies 4.8 and E supplies 2.4. Each pair therefore totals 7.2 lakh, which is why the comparison reduces exactly and no rounding is involved.

Answer: the required ratio is 1 : 1.