In an exhibition, Almond buys a painting for Rs 20,000 and sells it to Olive for Rs 23,000. Olive then sells it to Sarah at double Almond's profit percentage. At what price should Sarah sell this painting to earn a profit of 8%?

Introduction / Context:
This is another chain transaction problem where the painting changes hands three times. Almond earns one profit percentage, Olive earns double that percentage, and finally Sarah wants to earn 8% profit on her purchase. The question requires us to track cost prices and selling prices step by step to find Sarah's required selling price. It tests careful use of percentage profit at different stages.

Given Data / Assumptions:

• Almond buys the painting for Rs 20,000.
• He sells it to Olive for Rs 23,000.
• Olive's profit percentage is double Almond's profit percentage.
• Sarah buys the painting from Olive at Olive's selling price.
• Sarah wants to earn 8% profit on her own cost price.
• We need Sarah's selling price that gives her 8% profit.

Concept / Approach:
First, determine Almond's profit percentage using his cost and selling price. Then double this percentage to get Olive's profit percentage. Use Olive's percentage to compute her selling price to Sarah and confirm that it matches the given information. This selling price is Sarah's cost price. Finally, apply 8% profit on Sarah's cost price to find the price at which she must sell the painting. Each step uses the formula SP = CP * (1 + profit%).

Step-by-Step Solution:
Step 1: Almond's cost price = Rs 20,000, selling price to Olive = Rs 23,000.Step 2: Almond's profit = 23,000 - 20,000 = Rs 3,000.Step 3: Almond's profit percentage = (3,000 / 20,000) * 100 = 15%.Step 4: Olive's profit percentage is double Almond's, so Olive's profit% = 30%.Step 5: Olive bought the painting for Rs 23,000, so she sells it to Sarah at SP = 23,000 * 1.30 = Rs 29,900 (this is Sarah's cost price).Step 6: Sarah wants an 8% profit, so her selling price must be SP_Sarah = 29,900 * 1.08 = Rs 32,292.

Verification / Alternative check:
Check Sarah's profit: Profit = 32,292 - 29,900 = Rs 2,392. Profit% = (2,392 / 29,900) * 100 ≈ 8%. This confirms that Rs 32,292 is the correct selling price for Sarah to achieve an 8% profit. The earlier steps also align: Olive earns 30% profit on 23,000, giving 23,000 * 1.30 = 29,900, so all transaction stages are consistent.

Why Other Options Are Wrong:
Other values like Rs 34,410, Rs 31,184 and Rs 29,999 correspond to profit percentages different from 8%. For instance, selling at Rs 34,410 would give Sarah a much higher profit than 8%, while Rs 29,999 might give little or no profit. Only Rs 32,292 results in exactly 8% profit over her cost price of Rs 29,900.

Common Pitfalls:
Some learners might mistakenly double Almond's profit amount instead of his profit percentage for Olive, or they may treat Olive's selling price as 23,000 + 3,000 rather than 30% of 23,000. Another frequent error is to apply Sarah's 8% on the original 20,000 instead of on her actual purchase price from Olive. Always apply each profit percentage to the correct individual cost price at that stage of the transaction chain.

Final Answer:
Sarah should sell the painting for Rs. 32,292 to earn an 8% profit.