If books bought at prices ranging from ₹200 to ₹260 are sold at prices ranging from ₹250 to 300, what is the greatest possible profit that might be made in selling 25 books?

Correct — A. The greatest profit comes from the cheapest buy paired with the dearest sale.

Lowest cost price available = ₹200
Highest selling price available = ₹300
Greatest profit per book = 300 − 200 = ₹100
Over 25 books: 100 × 25 = ₹2,500 → option (a)

Nothing in the stem ties a book's cost to its selling price, so every one of the 25 may be bought at ₹200 and sold at ₹300.

Why the others are wrong

• (b)
  ₹1,800 — ₹1,800 is ₹72 a book. That margin is reachable — buy at ₹208, sell at ₹280 — but it is not the greatest, which is what the stem asks for.
• (c)
  ₹2,300 — ₹2,300 is ₹92 a book, also attainable (₹208 to ₹300), but still short of the ₹100 ceiling set by the cheapest buy and dearest sale.
• (d)
  ₹2,700 — ₹2,700 needs ₹108 a book, which is impossible: the widest gap the two ranges allow is ₹300 − ₹200 = ₹100.

To maximise a difference when both quantities move over ranges, take the smallest value of what you subtract and the largest value of what you subtract it from.

Profit = selling price − cost price, so the maximum uses the lowest cost, ₹200, and the highest sale, ₹300. The two ranges are independent — the stem never says a dearer book must sell dearer.

The same reasoning run the other way gives the worst case: ₹250 − ₹260 = a ₹10 loss per book.

Key facts

• Cost prices run ₹200 to ₹260 and selling prices ₹250 to ₹300.
• Per-book profit can therefore range from a ₹10 loss (250 − 260) to a ₹100 gain (300 − 200).
• Greatest profit on 25 books = 25 × ₹100 = ₹2,500.

Common traps

• Pairing the wrong endpoints — ₹300 − ₹260 = ₹40 or ₹250 − ₹200 = ₹50 — instead of the widest gap.
• Averaging the ranges to ₹230 and ₹275 and calling ₹45 a book the answer.
• Assuming a costlier book must fetch a higher price, which the stem never states.

No directly related past PYQ was found.