Rs. 2600 is divided into three parts A, B and C in the ratio 1/2 : 1/3 : 1/4. By how much is share A greater than share C?

Introduction / Context:
This problem is about dividing a sum of money into three parts according to a ratio expressed with fractional terms. It tests the ability to convert fractional ratios into simple integer ratios and then compute exact amounts for each part before comparing them. Such questions are standard in aptitude and financial reasoning sections.

Given Data / Assumptions:
• Total amount to be divided = Rs. 2600.
• The ratio of A : B : C is 1/2 : 1/3 : 1/4.
• We must find how much more A receives compared to C.
• All shares are non-negative and sum to the total amount.

Concept / Approach:
Fractions are converted to a common base so that ratio terms become integers. The denominators are 2, 3 and 4. The least common multiple of these denominators is 12. By multiplying each fraction by 12, we can convert 1/2, 1/3 and 1/4 into 6, 4 and 3 respectively. These integers give us the ratio A : B : C = 6 : 4 : 3. Then we distribute Rs. 2600 according to these 6 + 4 + 3 = 13 parts, and finally compute the difference between A and C.

Step-by-Step Solution:
Step 1: Original ratio is 1/2 : 1/3 : 1/4.Step 2: Convert each fraction using LCM of denominators 2, 3 and 4, which is 12.Step 3: Multiply each fraction by 12: (1/2)*12 = 6, (1/3)*12 = 4, (1/4)*12 = 3. So ratio becomes A : B : C = 6 : 4 : 3.Step 4: Total ratio parts = 6 + 4 + 3 = 13.Step 5: Value of one part = 2600 / 13 = 200.Step 6: Share of A = 6 * 200 = Rs. 1200; share of C = 3 * 200 = Rs. 600.Step 7: Difference A − C = 1200 − 600 = Rs. 600.

Verification / Alternative check:
We can also compute B to confirm the sum: B = 4 * 200 = Rs. 800. Then total = 1200 + 800 + 600 = Rs. 2600, which matches the original amount. This confirms that our conversion of the fractional ratio to integer parts and subsequent calculations are correct.

Why Other Options Are Wrong:
Option 300 would imply A is only Rs. 300 more than C, which would require different underlying shares than 1200 and 600. That contradicts the ratio 6 : 4 : 3 derived from the fractions.
Options 150 and 75 similarly do not match the true difference obtained from correctly dividing the amount according to the given ratio.

Common Pitfalls:
One common error is to treat the fractional ratio values directly as the shares without converting to simple integers, which leads to incorrect partitioning. Another mistake is to divide Rs. 2600 by the sum of the denominators instead of the sum of the scaled integer parts. Always convert fractions to an equivalent integer ratio before distributing the total amount.

Final Answer:
Share A is greater than share C by Rs. 600.