A shopping mall owner reduces the price of electronic goods by 20% to increase sales. As a result, the sales volume of electronics increases by 40%, and his weekly collection increases by Rs. 1,05,000. By how much did his gross collection increase per day, assuming a 7-day week?

Introduction / Context:
This problem involves the combined effect of a price decrease and a quantity increase on total revenue or collection. Such questions test understanding of percentage change in price and demand, and how they interact to affect overall earnings. After finding the overall percentage change, we connect it with the given increase in weekly collection and finally convert that to a daily amount.

Given Data / Assumptions:

Price of electronic goods is decreased by 20%.
Sales volume of electronics increases by 40%.
Total weekly collection increases by Rs. 1,05,000.
We need the increase in daily collection, assuming 7 days in a week.
All collections are in rupees and we consider only the effect of this change.

Concept / Approach:
Let the original weekly collection be R. When the price decreases by 20%, the new price factor is 0.8 of the old price. When sales increase by 40%, the new quantity factor is 1.4 of the old quantity. The new revenue is proportional to price factor multiplied by quantity factor, so we compute 0.8 * 1.4 to find the overall revenue multiplier. Then we use the information about the weekly increase (Rs. 1,05,000) to solve for R and then find the daily increase by dividing by 7.

Step-by-Step Solution:
Step 1: Represent price and quantity changes as multipliers. Price decreases 20%, so price factor = 1 - 0.20 = 0.8. Sales increase 40%, so quantity factor = 1 + 0.40 = 1.4. Step 2: Find the overall revenue multiplier. New revenue factor = 0.8 * 1.4 = 1.12. This means revenue increases by 12% overall. Step 3: Let the original weekly collection be R. New weekly collection = 1.12 * R. Increase in weekly collection = 1.12R - R = 0.12R. Given that this increase is Rs. 1,05,000, so 0.12R = 1,05,000. Step 4: Solve for R. R = 1,05,000 / 0.12. R = 8,75,000. Step 5: The weekly increase is given as 1,05,000, so the daily increase is 1,05,000 / 7. Daily increase = 15,000. Thus, the gross collection increased by Rs. 15,000 per day.

Verification / Alternative check:
We can also compute the new weekly revenue directly. Original weekly revenue is R = 8,75,000. A 12% increase gives new revenue = R + 0.12R = 1.12R = 1.12 * 8,75,000 = 9,80,000. The difference between 9,80,000 and 8,75,000 is 1,05,000, which matches the given weekly increase. Dividing 9,80,000 by 7 gives 1,40,000 per day after the change, while 8,75,000 / 7 gives 1,25,000 per day originally. The difference is 15,000 per day, confirming our answer.

Why Other Options Are Wrong:
Amounts like 14,400 or 14,600 per day imply different weekly increases when multiplied by 7, and they would not match the stated increase of 1,05,000.
14,800 per day gives a weekly increase of 1,03,600, which is a little short of the given figure.
16,000 per day would correspond to a weekly increase of 1,12,000, more than the stated increase.

Common Pitfalls:
A frequent mistake is to add or subtract the percentages directly (for example, 40 minus 20 = 20%) and assume a 20% change in revenue, which is incorrect. Another error is to treat the 1,05,000 as the new weekly collection rather than the increase. Some learners also divide by 5 instead of 7 when computing the daily change. Always remember that combined percentage changes must be handled by multiplying their factors, and that revenue is proportional to both price and quantity together.

Final Answer:
The gross collection increased by Rs. 15,000 per day.