Discussion

Question:

When the sale price of an item was increased by 50%, there was a decrease of 20% in its sales quantity. What was the percentage effect on the sales?

Explanation:

Let p be the price/unit (Rs./ unit) q be the quantity sold (units)

Then sales = pq (Rs./Unit . Unit)

After price and quantity changes, new price = 1.5p and new quantity = 0.8q

Total sales after these changes = 1.5p × 0.8q

Hence, % effect on sales = $\frac{1.5 p \times 0.8 q}{p q}$ = 1.2

⇒ Sales increased by 20%.

Alternately,

Net change = 50 - 20 + $\frac{50 \times - 20}{100}$ = 20

Hence, option (a).

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