Coins inheritance and post-change ratio: Mr. Shrimant has 2505 gold coins divided among his sons Bharat, Parat, and Marat. Afterwards, Bharat sells 30 coins, Parat donates 30 coins, and Marat loses 25 coins. The numbers then stand in the ratio 46 : 41 : 34. How many coins did Parat originally receive?

Introduction / Context:
This problem mixes a total-sum constraint with a ratio that applies after specific adjustments to each person’s count. The key is to convert the post-change ratio into equations for the original numbers and then use the overall total to solve for the scaling factor.

Given Data / Assumptions:

• Total coins initially = 2505.
• Post-change ratio (Bharat : Parat : Marat) = 46 : 41 : 34.
• Adjustments: Bharat −30, Parat −30, Marat −25 (respectively).

Concept / Approach:
Let the post-change numbers be 46t, 41t, and 34t. Then original numbers are Bharat = 46t + 30, Parat = 41t + 30, Marat = 34t + 25. The sum of originals equals 2505, which will determine t. Then compute Parat’s original figure.

Step-by-Step Solution:
(46t + 30) + (41t + 30) + (34t + 25) = 2505.121t + 85 = 2505 ⇒ 121t = 2420 ⇒ t = 20.Parat originally = 41t + 30 = 820 + 30 = 850.

Verification / Alternative check:
Originals: 46*20+30 = 950; 41*20+30 = 850; 34*20+25 = 705; total = 2505, consistent.

Why Other Options Are Wrong:

• 705 and 950 are Marat’s and Bharat’s initial counts, not Parat’s.
• 800 does not satisfy the total when paired with the others.

Common Pitfalls:

• Applying +30 instead of −30 (or vice versa) to the wrong son.
• Forgetting to add back lost/donated/sold coins to reach original counts.

Final Answer:
850