Question

Two shopkeepers sell the same article at the same price for the same quantity. One gives $25\%$ discount; the other offers $25\%$ more quantity at the same price. From a customer's view, which is better?

• A. 1st shopkeeper's deal
• B. 2nd shopkeeper's deal
• C. both are equal
• D. cannot be determined

Hint:

"More quantity at same price" $\Rightarrow$ divide price by the quantity factor to get the effective price per unit.

Answer 1

The Correct Option is A

Deal 1: price becomes $75\%$ of original (effective price factor $0.75$).
Deal 2: quantity becomes $125\%$; effective price per unit $=\frac{1}{1.25}=0.80$ of original.
Since $0.75 < 0.80$, Deal 1 is better. 

Answer 2

Instead of comparing the effective price factors algebraically, we can compare the two deals using a concrete numerical example, then check each option against it.

1. Option A (1st shopkeeper's deal): Suppose the original price is ₹\(100\) for \(4\) units (so ₹\(25\) per unit). Under the first shopkeeper's \(25\%\) discount, the customer pays ₹\(75\) for the same \(4\) units, i.e. ₹\(18.75\) per unit. Under the second shopkeeper's offer, the customer pays the same ₹\(100\) but receives \(25\%\) more quantity, i.e. \(5\) units, i.e. ₹\(20\) per unit. Since ₹\(18.75\) per unit is cheaper than ₹\(20\) per unit, the first shopkeeper's deal is better for the customer.
2. Option B (2nd shopkeeper's deal): As shown, the effective per-unit price here (₹\(20\)) is higher than the first deal's (₹\(18.75\)), so this deal is not the better one.
3. Option C (both equal): The two per-unit prices, ₹\(18.75\) and ₹\(20\), are different, so the deals are not equal.
4. Option D (cannot be determined): Since concrete numbers give a definite comparison, the better deal can indeed be determined.

The numerical comparison confirms that discounting the price works out cheaper for the customer than the equivalent quantity bonus.

Hence, the correct answer is option A: 1st shopkeeper's deal.