If three eighth of a number is 141, then what is the approximate value of 32.08% of that number?

Introduction / Context:
This question combines fractions and percentages. First, we are given that three eighth of a number equals 141, and we must find the approximate value of 32.08% of the same number. Such problems are common in aptitude exams and test a student's ability to move comfortably between fraction based information and percentage based requirements.

Given Data / Assumptions:

• Three eighth of a number N is 141.
• That is, (3 / 8) * N = 141.
• We must find the approximate value of 32.08% of N.
• Approximation is allowed, so choosing the closest option is acceptable.

Concept / Approach:
First, we use the fraction equation (3 / 8) * N = 141 to solve for N. Once we know N, we compute 32.08% of N by converting 32.08% to its decimal form and multiplying by N. Finally, we compare the numeric result to the given options and choose the closest value. This method ensures accurate use of both fractional and percentage information.

Step-by-Step Solution:
Step 1: Given (3 / 8) * N = 141. Step 2: Solve for N: N = 141 * (8 / 3). Step 3: Compute 141 * 8 = 1128. Step 4: Divide by 3: 1128 / 3 = 376, so N = 376. Step 5: We need 32.08% of N, that is 32.08% of 376. Step 6: Convert 32.08% to decimal: 32.08% = 32.08 / 100 = 0.3208. Step 7: Compute 0.3208 * 376. Step 8: 0.3208 * 376 ≈ 120.6208. Step 9: The approximate value is about 121, but among the given options, 120 is the closest.

Verification / Alternative check:
We can approximate the percentage slightly. 32.08% is close to 32%. 32% of 376 is 0.32 * 376. Now, 0.32 * 376 = 120.32. This again is close to 120 and consistent with the more exact calculation of about 120.62. So, whether we consider 32% or 32.08%, the nearest integer is around 120, confirming the choice of 120 as the best approximation.

Why Other Options Are Wrong:
101, 112, 104, and 130 are either too low or too high compared to 120.62. For example, 112 is around 8 or 9 units away, while 130 overshoots by nearly 9 or 10 units. Among the listed options, 120 is the closest to the computed value of 120.6208, so it is the best approximation and the only correct answer in the context of this question.

Common Pitfalls:
One common mistake is to solve (3 / 8) * N = 141 incorrectly, for example by multiplying by 3 / 8 instead of 8 / 3 when isolating N. Another pitfall is to misconvert the percentage 32.08% into decimal form, perhaps writing 0.03208 rather than 0.3208. Finally, ignoring the instruction about approximation and expecting an exact match in the options can cause confusion. Always compute carefully and then choose the closest option when approximation is implied.

Final Answer:
The approximate value of 32.08% of the number is 120.