What is the numerical value of 10% of 150% of 400, when the percentages are applied in sequence to the number 400?

Introduction / Context:
This question checks understanding of how to handle successive percentages applied to a base number. The phrase “10% of 150% of 400” means that we first calculate 150% of 400 and then take 10% of that result. Problems like this are important in many quantitative topics, including compound percentage situations, multi stage discounts, and interest calculations. Correct interpretation of the order of operations is crucial for arriving at the right answer.

Given Data / Assumptions:

• Base number = 400.
• We first compute 150% of 400.
• Then we compute 10% of the result obtained in the first step.
• All percentages are applied in the standard arithmetic way.

Concept / Approach:
Percentages can always be converted into fraction or decimal form. One effective approach is to write 150% as 150 / 100 and 10% as 10 / 100. Then apply these step by step to the base number. Alternatively we can combine the percentage multipliers into a single factor before applying them to the base. Both methods give the same final result if executed correctly. This problem does not involve any tricky rounding or hidden information, it is purely about correct sequence and arithmetic.

Step-by-Step Solution:
Step 1: First find 150% of 400. Step 2: 150% of 400 = (150 / 100) * 400. Step 3: Simplify (150 / 100) * 400 = 1.5 * 400 = 600. Step 4: Now we need 10% of this result, which is 10% of 600. Step 5: 10% of 600 = (10 / 100) * 600. Step 6: Simplify (10 / 100) * 600 = 0.1 * 600 = 60. Step 7: Therefore the value of 10% of 150% of 400 is 60. Step 8: We can also combine the calculation: overall factor = (10 / 100) * (150 / 100) = 1500 / 10000 = 0.15, and 0.15 * 400 = 60.

Verification / Alternative check:
We have verified by two approaches. The first approach applies percentages stepwise, and the second approach multiplies the percentage factors before applying them to 400. In both ways the final result is 60. There is no ambiguity about order because the phrase clearly states “10% of 150% of 400,” which means 10% of the quantity that is 150% of 400. If we mistakenly took 150% of 10% of 400 instead, we would compute a different value, but that would not follow the wording given.

Why Other Options Are Wrong:
If the answer were 600, that would correspond to 150% of 400 without taking the final 10%. The value 50 does not arise from any natural miscalculation here. The value 500 would suggest replacing 150% by 125% or similar error. Only 60 matches the correct computation of 10% of 600. Thus, among the options provided, 60 is the only correct result that fits the stepwise percentage operations stated in the problem.

Common Pitfalls:
A common mistake is to misread “10% of 150% of 400” as simply 160% of 400 or as 10% plus 150% of 400. Another frequent error is to treat both percentages as added instead of multiplied. Learners also sometimes forget that the outer percentage operates on the intermediate result, not on the original number again. Writing everything explicitly as fractions or decimals helps maintain clarity and prevents such errors.

Final Answer:
The correct value of 10% of 150% of 400 is 60.