Three friends divide Rs. 624 in the ratio 1/2 : 1/3 : 1/4. What is the share of the third friend?

Introduction / Context:
Ratios can be given as fractions. The amounts received are proportional to these fractional numbers. The process is to convert the fractional ratio into proportional parts, total those parts, and then distribute the total sum accordingly.

Given Data / Assumptions:

• Total amount = Rs. 624
• Ratio among three friends = 1/2 : 1/3 : 1/4
• “Third friend” corresponds to the 1/4 part in the given ratio order.

Concept / Approach:
If the ratio is a : b : c, then shares are (a/total of ratio) * sum, etc. Here, a = 1/2, b = 1/3, c = 1/4. First compute a + b + c, then the third share = (c / (a + b + c)) * 624.

Step-by-Step Solution:
Sum of ratio terms = 1/2 + 1/3 + 1/4 = 6/12 + 4/12 + 3/12 = 13/12Third share fraction of total = (1/4) / (13/12) = (1/4) * (12/13) = 12/52 = 3/13Third share = 624 * (3/13) = 48 * 3 = Rs. 144

Verification / Alternative check:
Compute first and second shares similarly and confirm that all three add to Rs. 624.

Why Other Options Are Wrong:
Rs. 288 and Rs. 192 correspond to other parts or doubled values; Rs. 148 and Rs. 156 are rounding guesses not matching exact proportional division.

Common Pitfalls:
Adding the numerators directly without common denominators; treating 1/2 : 1/3 : 1/4 as 1 : 1 : 1 inadvertently.

Final Answer:
Rs. 144