Two shopkeepers both mark a sewing machine at Rs. 700. The first shopkeeper offers successive discounts of 30% and 6%, while the second offers successive discounts of 20% and 16%. What is the difference between the two final selling prices?

Introduction / Context:
This question compares two different schemes of successive discounts on the same marked price. Students must compute each shopkeeper's final selling price and then find the difference between the two. It reinforces the idea that successive discounts multiply and are not simply added, and it highlights how different discount structures can produce different effective price reductions even if the total of the percentages looks similar.

Given Data / Assumptions:

• Marked price of the sewing machine = Rs. 700 for both shopkeepers.
• First shopkeeper offers two successive discounts: 30% and 6%.
• Second shopkeeper offers two successive discounts: 20% and 16%.
• We must find the absolute difference between their final selling prices.

Concept / Approach:
A discount of d% on a price P means the new price is P * (1 − d/100). When there are successive discounts, we multiply the factors corresponding to each discount. For example, discounts of 30% and 6% correspond to multiplying the marked price by 0.70 and then by 0.94. We compute each shopkeeper's final selling price separately using the respective compound discount factors and then subtract the smaller selling price from the larger one to find the difference.

Step-by-Step Solution:
Marked price MP = Rs. 700.First shopkeeper: discounts 30% and then 6%.First discount factor = 1 − 30/100 = 0.70; second factor = 1 − 6/100 = 0.94.Final selling price S1 = 700 * 0.70 * 0.94.Compute: 700 * 0.70 = 490; then 490 * 0.94 = 460.6.Second shopkeeper: discounts 20% and then 16%.Discount factors: 1 − 20/100 = 0.80 and 1 − 16/100 = 0.84.Final selling price S2 = 700 * 0.80 * 0.84.Compute: 700 * 0.80 = 560; then 560 * 0.84 = 470.4.Difference between selling prices = S2 − S1 = 470.4 − 460.6 = Rs. 9.8.

Verification / Alternative check:
Instead of computing intermediate values, we can directly multiply the factors with 700.For the first shopkeeper: 700 * (0.70 * 0.94) = 700 * 0.658 = 460.6.For the second shopkeeper: 700 * (0.80 * 0.84) = 700 * 0.672 = 470.4.Difference remains 470.4 − 460.6 = Rs. 9.8, confirming the earlier result.

Why Other Options Are Wrong:
Rs. 16.8, Rs. 22.4, and Rs. 36.4 arise from incorrect handling of percentage discounts or from assuming a single equivalent discount rather than successive ones.Only Rs. 9.8 matches the precise computed difference between S1 and S2.

Common Pitfalls:
A common mistake is to subtract percentage discounts (for example, 30% + 6% = 36%) and apply that directly, which ignores the compounding effect.Another error is to apply both shopkeepers' discounts to the same intermediate price instead of recalculating individually from the marked price.Rounding too early in calculations can also lead to small deviations, pushing the answer away from the correct option.

Final Answer:
The difference between the final selling prices offered by the two shopkeepers is Rs. 9.8.