If P is 140 and this value is 40% more than Q, then what is the value of (3/25) of Q?

Introduction / Context:
This question joins percentage comparison between two variables with a fractional calculation on one of them. It is a typical aptitude style problem where you need to interpret "40% more than" correctly, find the unknown quantity, and then compute a fraction of it. Such problems help reinforce both percentage and fraction skills, which are essential for a wide range of quantitative topics.

Given Data / Assumptions:

• P is given as 140.
• P is 40% more than Q.
• We must find the value of (3/25) * Q.
• No other conditions or constraints are given.

Concept / Approach:
When a quantity P is 40% more than Q, it means P = Q + 40% of Q = 1.4 * Q. From this equation, we can solve for Q by dividing P by 1.4. Once Q is known, computing (3/25) * Q is straightforward. The key concept is to correctly interpret the phrase "40% more than" as a multiplicative relationship, not a simple difference without reference to Q.

Step-by-Step Solution:
Step 1: Given P = 140.Step 2: P is 40% more than Q, so P = 1.4 * Q.Step 3: Substitute P = 140 into the equation: 140 = 1.4 * Q.Step 4: Solve for Q by dividing both sides by 1.4: Q = 140 / 1.4.Step 5: 140 / 1.4 = 100, so Q = 100.Step 6: Now compute (3/25) of Q: (3/25) * Q = (3/25) * 100.Step 7: (3/25) * 100 = 3 * (100 / 25) = 3 * 4 = 12.Step 8: Therefore, (3/25) of Q is 12.

Verification / Alternative check:
To verify, we can start from Q = 100 and check the relationship with P. If Q is 100, then 40% of Q is 40, and 40% more than Q is Q + 40 = 140. This matches the given value of P. Next, computing (3/25) of Q as 3/25 * 100 directly gives 12, confirming that the calculations and the interpretation of "40% more than" are correct.

Why Other Options Are Wrong:
If we tried 9, then Q would incorrectly be treated such that 3/25 of Q equals 9, implying Q = 75, which does not satisfy the relation P = 140 = 1.4 * 75. Option 18 would imply Q = 150, giving P = 1.4 * 150 = 210, not 140. Option 24 implies Q = 200, giving P = 280, again inconsistent. Option 15 implies Q = 125, with P = 175, not 140. Thus none of these values satisfy all given conditions except 12.

Common Pitfalls:
Some learners misinterpret "P is 40% more than Q" as P = Q + 40, rather than P = Q + 0.4 * Q, which leads to incorrect equations. Others might invert the relationship and treat Q as 40% more than P. A further error is to compute 3/25 of P rather than of Q. To avoid these mistakes, carefully translate verbal percentage phrases into algebraic expressions and track which variable is being compared to which.

Final Answer:
The value of (3/25) of Q is 12.