A bookseller sells a book at a gain of 10%. If he had bought it at 4% less and sold it for ₹6 more, he would have gained 18 3/4% (recovered assumption for a consistent solvable stem). What is the cost price (CP) of the book?

Introduction / Context:
Problems of this type compare two nearby scenarios with small tweaks to cost and selling price, resulting in a different profit percentage. By modeling both cases with variables, one can set up an equation that eliminates the selling price and reveals the true cost price. The original statement had a conflicting percentage; under the Recovery-First Policy, interpreting it as 18 3/4% (i.e., 18.75%) makes the data consistent and solvable.

Given Data / Assumptions:

• Actual sale at 10% gain: SP₁ = 1.10 * CP = 1.10x
• Alternate case: CP′ = 0.96x (4% less), SP′ = SP₁ + ₹6
• Alternate gain% = 18.75% on CP′ ⇒ SP′ = 1.1875 * CP′

Concept / Approach:
Equate SP′ from both expressions and solve for x (the original CP). This approach leverages linear relations between cost and selling price and uses percentage conversions accurately.

Step-by-Step Solution:
SP′ = 1.1875 * (0.96x) = 1.14xBut SP′ = SP₁ + 6 = 1.10x + 6Therefore, 1.10x + 6 = 1.14x ⇒ 6 = 0.04x ⇒ x = ₹150

Verification / Alternative check:
At CP = ₹150: actual SP₁ = ₹165 (10% gain). Alternate CP′ = ₹144 and alternate SP′ (1.1875 of 144) = ₹171. SP₁ + 6 = 165 + 6 = 171 — consistent with the scenario.

Why Other Options Are Wrong:
₹130/₹140/₹160 do not satisfy the equation 1.10x + 6 = 1.14x under the recovered 18.75% condition.

Common Pitfalls:
Applying the 4% to selling price instead of cost; reading the percentage as 11 3/4% or 118 3/4% which makes the problem inconsistent; failing to convert 18 3/4% to 0.1875 decimal form accurately.

Final Answer:
₹ 150