The selling price of a cellphone is increased by 20 percent, and as a result the number of units sold decreases by 30 percent. What is the net percentage change in total sales revenue for the shopkeeper?

Introduction / Context:
This problem tests understanding of percentage change in revenue when both price and quantity change. It is a classic type of question in profit and loss where candidates must recognize that revenue is the product of price and quantity, and changes in both factors can result in an overall gain or loss.

Given Data / Assumptions:

• Original selling price of each cellphone = P (assumed).
• Original number of units sold = Q (assumed).
• Price is increased by 20 percent, so new price = 1.20 * P.
• Quantity sold decreases by 30 percent, so new quantity = 0.70 * Q.
• We need the net percentage change in total sales revenue.

Concept / Approach:
Total revenue is calculated as price multiplied by quantity. When both price and quantity change, the new revenue is the product of the new price and new quantity. The percentage change in revenue is then found by comparing new revenue with old revenue using the standard percentage change formula.

Step-by-Step Solution:
Original revenue = P * Q. New price after 20 percent increase = 1.20 * P. New quantity after 30 percent decrease = 0.70 * Q. New revenue = (1.20 * P) * (0.70 * Q) = 0.84 * P * Q. Thus new revenue is 84 percent of the original revenue. Percentage change in revenue = (new - old) / old * 100. Percentage change = (0.84 * P * Q - 1 * P * Q) / (P * Q) * 100. Percentage change = (0.84 - 1.00) * 100 = -16 percent. This means there is a 16 percent decrease in total sales revenue.

Verification / Alternative check:
Take convenient numbers: let P = Rs. 100 and Q = 10 units. Original revenue = 100 * 10 = Rs. 1000. New price = 120 rupees, new quantity = 7 units. New revenue = 120 * 7 = Rs. 840. Change in revenue = 840 - 1000 = -160 rupees. Percentage change = -160 / 1000 * 100 = -16 percent. This confirms a 16 percent loss in revenue.

Why Other Options Are Wrong:
14.5%: This value does not match the product of the two percentage multipliers. 12% and 10.5%: These are smaller decreases and typically result from incorrect addition or subtraction of percentage values instead of multiplying them. Only 16 percent correctly reflects the combined effect of a 20 percent increase in price and a 30 percent fall in quantity.

Common Pitfalls:
Candidates sometimes add or subtract percentages directly, for example doing 20 percent minus 30 percent to get 10 percent, which is completely wrong in a revenue problem. Another common error is to forget that percentage changes in price and quantity must be combined multiplicatively, not additively. Always use the formula new revenue factor = price factor * quantity factor.

Final Answer:
The total sales revenue decreases by 16%, so the net effect is a 16 percent loss.