King Ajay distributes his gold among his three queens by giving 50% of his wealth to the first queen, 50% of the remaining gold to the second queen, and again 50% of the remaining gold to the third queen. If the combined share of the three queens is 1,30,900 kilograms of gold, what was the total quantity of gold King Ajay originally had?

Introduction / Context:
This is a percentage and fraction based distribution problem involving successive sharing of wealth. The question describes how King Ajay distributes his gold among three queens by repeatedly giving half of the remaining amount. Such problems are common in aptitude exams and test understanding of fractions, percentages, and reverse calculations when the final distributed amount is known but the initial amount is unknown.

Given Data / Assumptions:

• Let the initial amount of gold be G kilograms.
• First queen receives 50% of G, which is G / 2.
• Second queen receives 50% of the remaining gold.
• Third queen receives 50% of what remains after the second queen receives her share.
• The total quantity received by all three queens together is 1,30,900 kilograms of gold.

Concept / Approach:
The main idea is to model the distribution process as fractions of the original amount G. Because each queen receives half of what is available at her turn, we can express each queen's share in terms of G and then sum those expressions. After that, we set the sum equal to the given combined share of 1,30,900 kilograms and solve for G. This method is often easier and safer than trying to work backward step by step without algebra.

Step-by-Step Solution:
Step 1: Let the total initial gold be G kilograms. Step 2: First queen gets 50% of G, so her share = G / 2. Remaining gold = G - G / 2 = G / 2. Step 3: Second queen gets 50% of the remaining G / 2, so her share = (1 / 2) * (G / 2) = G / 4. Remaining gold = G / 2 - G / 4 = G / 4. Step 4: Third queen gets 50% of the remaining G / 4, so her share = (1 / 2) * (G / 4) = G / 8. Remaining gold after this is G / 4 - G / 8 = G / 8. Step 5: Total gold given to the queens = G / 2 + G / 4 + G / 8 = (4G / 8 + 2G / 8 + G / 8) = 7G / 8. Step 6: We are told that 7G / 8 = 130900. Step 7: Solve for G: G = 130900 * (8 / 7) = 149600. Step 8: Therefore, King Ajay originally had 1,49,600 kilograms of gold.

Verification / Alternative check:
We can forward check using G = 149600. First queen: 50% of 149600 = 74800. Remaining = 74800. Second queen: 50% of 74800 = 37400. Remaining = 37400. Third queen: 50% of 37400 = 18700. Total given = 74800 + 37400 + 18700 = 130900, which matches the given combined share. This confirms that the calculated initial wealth is correct.

Why Other Options Are Wrong:
Values like 153145 kgs, 147890 kgs, and 152400 kgs do not produce a combined share of exactly 130900 kilograms when the same pattern of distribution is applied. The option 140000 kgs is a round figure but also fails to yield the correct total. Only 149600 kgs reproduces the given final combined share, so it is the correct answer.

Common Pitfalls:
A common mistake is to assume that the total given is simply 50% + 50% + 50% of the original amount, which would wrongly suggest that 150% of the gold was distributed. The key is that each 50% is taken from the current remainder, not from the original amount every time. Another error is to miscalculate the fraction sum 1 / 2 + 1 / 4 + 1 / 8, which must be carefully handled as 7 / 8.

Final Answer:
The total quantity of gold King Ajay originally had was 149600 kgs.