Final answer:
To find the overall percentage increase after successive increases of 30% and then 40%, you multiply 1.30 by 1.40 to get a final multiplier of 1.82, indicating an 82% increase overall, which is not one of the provided options.
Step-by-step explanation:
To determine the overall percentage increase when you first increase an amount by 30% and then by 40%, you can use multipliers. The multiplier for a 30% increase is 1.30 (100% + 30%), and the multiplier for a subsequent 40% increase is 1.40 (100% + 40%). You multiply the original amount by both multipliers in sequence to find the overall effect.
Let's do the math:
Initial multiplier (after 30% increase) = 1.30
Second multiplier (after additional 40% increase) = 1.40
Overall multiplier = 1.30 × 1.40 = 1.82
The overall multiplier of 1.82 means that the final amount is 182% of the original, which corresponds to an 82% increase from the original amount. Therefore, the correct answer is none of the given options (a) 60%, (b) 70%, (c) 72%, or (d) 74%