Final answer:
The correct number of pensioners in a sample of 315 should be calculated by combining the ratios of children:adults and adults:pensioners, which results in 153 pensioners. However, this is not one of the options, suggesting an error in the provided choices or the calculation.
Step-by-step explanation:
To determine the number of pensioners that should be in the sample, we need to calculate the ratios of children to adults and adults to pensioners and combine these to find the overall ratio of children, adults, and pensioners. Then, we can find the proportion of pensioners to the total and use this to calculate how many pensioners should be in a sample of 315.
First, we have the ratio of children to adults as 2:5. Next, the ratio of adults to pensioners as 3:4. To combine these ratios to include all three groups, we can equate the adult's part of both ratios to find a common value, which will be the least common multiple of 5 and 3, which is 15. This means we'll scale the first ratio (children:adults) by multiplying by 3 to get 6:15 and the second ratio (adults:pensioners) by multiplying by 5 to get 15:20.
So, the combined ratio of children:adults:pensioners is 6:15:20. The sum of these parts is 6 + 15 + 20 = 41 parts. The part for pensioners is 20/41 of the entire ratio.
Since we are taking a sample of 315 people, we calculate the number of pensioners as follows: (20/41) * 315 = 20 * 7.68 (approx) = 153.6, which rounds down to 153, because we cannot have a fraction of a person.
Therefore, the calculated number of pensioners in the stratified sample is not one of the options provided, indicating there may be an error in the options given or in the calculation. We expect an answer of 153 pensioners, but the closest option is 140, which is option d.