Final answer:
B's share of the income is Rs. 450. This is found by first calculating the total expenditure and then applying the given ratio and savings percentage to determine each individual's share of income, which adds up to the total income of Rs. 1530.
Step-by-step explanation:
The student is asking to find B's share of income, given that A, B, and C have a total income of Rs. 1530 and that they save 20%, 25%, and 40% of their income, respectively.
The expenditure ratio for A, B, C is 16:12:9. To find B's income share, first we calculate the total expenditure based on their income and savings, then apply the ratio to determine each individual's expenditure, and hence their income after savings.
Let's consider their total expenditure to be 'x'. Then, A's expenditure is (16/37)x, B's is (12/37)x, and C's is (9/37)x. The income for A, B, and C would be (16/37)x/(1-0.20), (12/37)x/(1-0.25), and (9/37)x/(1-0.40) respectively, because they save 20%, 25%, and 40%. The sum of these incomes is equal to 1530.
To find the total expenditure 'x', we solve the following equation:
(16/37)x/(0.80) + (12/37)x/(0.75) + (9/37)x/(0.60) = 1530. Solving for 'x' gives us the total expenditure.
Now we can find the share of B's income by calculating (12/37)x/(1-0.25).
After calculating, B's share of the income turns out to be Rs. 450, which corresponds to option b).