Three independent cost-cutting strategies P, Q and R are applied in a company. Strategy P reduces costs by 20%, Q reduces the (already reduced) cost by 30%, and R further reduces it by 10%. Assuming all three strategies operate independently and sequentially, what is the net percentage saving achieved?

Introduction / Context:
This problem explores the combined effect of multiple successive percentage reductions on cost. Each strategy independently cuts costs by a given percentage and acts on the currently reduced amount, not on the original. The question asks for the net saving after all strategies have been applied. This is a classic example of successive percentage change where multiplicative factors must be used instead of simple addition of percentages.

Given Data / Assumptions:

• Strategy P saves 20%, so it leaves 80% of the cost.
• Strategy Q saves 30%, so it leaves 70% of the cost it acts on.
• Strategy R saves 10%, so it leaves 90% of the cost it acts on.
• The strategies are applied one after another, each acting on the cost remaining after the previous strategy.
• We must find the overall percentage saving compared to the original cost.

Concept / Approach:
Let the original cost be C. After strategy P, the cost is 0.80 * C. After strategy Q, it becomes 0.70 of that, and after strategy R, it becomes 0.90 of the already reduced cost. So final cost = C * 0.80 * 0.70 * 0.90. The net saving is then original cost minus final cost, and the net percentage saving is that difference divided by original cost, multiplied by 100. Because each strategy acts multiplicatively, we must multiply their remaining fractions to get the final factor.

Step-by-Step Solution:
Step 1: Let original cost = C. Step 2: After strategy P (20% saving), remaining cost = 80% of C = 0.80 * C. Step 3: After strategy Q (30% saving), remaining cost = 70% of the current amount = 0.70 * (0.80 * C). Step 4: After strategy R (10% saving), remaining cost = 90% of the current amount = 0.90 * [0.70 * (0.80 * C)]. Step 5: Combine the factors: final cost = C * 0.80 * 0.70 * 0.90. Step 6: Compute the product: 0.80 * 0.70 = 0.56. Step 7: Now 0.56 * 0.90 = 0.504. Step 8: Thus, final cost = 0.504 * C. Step 9: Net saving fraction = 1 - 0.504 = 0.496. Step 10: Net percentage saving = 0.496 * 100 = 49.6%.

Verification / Alternative check:
Take an example with C = 100 units. After strategy P, cost is 80. After applying Q, cost is 70% of 80, which is 56. After R, cost is 90% of 56, which is 50.4. Net saving = 100 - 50.4 = 49.6. Expressed as a percentage of the original 100, this is 49.6%. The example confirms the algebraic result and matches option 49.6%.

Why Other Options Are Wrong:
50.4% would be the percentage of cost remaining, not the percentage saved. 33.67% or 66.66% do not correspond to the calculated net savings and likely stem from adding or subtracting percentages instead of multiplying remaining fractions. The correct combined effect of 20%, 30% and 10% savings is a 49.6% overall saving.

Common Pitfalls:
A very common mistake is to simply add the three savings and say 20 + 30 + 10 = 60% saving. This ignores the fact that each subsequent strategy acts on an already reduced cost. Another mistake is to add the remaining percentages (80, 70, 90) and attempt to average them, which does not reflect the multiplicative effect. Always convert each saving into a remaining fraction and multiply them to get the final fraction of cost left.

Final Answer:
The net percentage saving achieved is 49.6%.