Maintaining a price ratio after changes: Prices of two articles are in the ratio 3 : 4. If the first increases by 10% and the second increases by ₹4 so that the original ratio remains 3 : 4, find the original price of the second article.

Introduction / Context:
This is a ratio preservation problem with a percentage change on one item and an absolute change on the other. We set unknowns for original prices, apply changes, and force the ratio to remain 3 : 4, then solve for the scale factor.

Given Data / Assumptions:

• Original prices: First = 3x, Second = 4x.
• Change: First increases by 10% ⇒ 3x becomes 3.3x.
• Change: Second increases by ₹4 ⇒ 4x becomes 4x + 4.
• Post-change ratio remains 3 : 4.

Concept / Approach:
Impose 3.3x : (4x + 4) = 3 : 4. Cross-multiply to get a linear equation in x and solve. The second’s original price is 4x.

Step-by-Step Solution:

Verification / Alternative check:
New prices: First = 33, Second = 44. Ratio 33 : 44 simplifies to 3 : 4, matching the condition.

Why Other Options Are Wrong:

• ₹10, ₹30, ₹35: Do not satisfy the preserved ratio when tested with the given changes.

Common Pitfalls:
Applying 10% to the ratio instead of the first price, or forgetting that ₹4 is an absolute change, not percentage-based.

Final Answer: