If Rs 25,000 is to be divided between A, B and C in the ratio 1/10 : 1/6 : 1/15, then how much (in Rs) will C receive?

Introduction / Context:
This is another ratio distribution problem where the ratio terms are given as fractions. A sum of money must be divided among three people A, B and C in the stated fractional ratio. We must find the share of C. The main challenge is handling the fractional nature of the ratio and converting it into a workable whole-number form.

Given Data / Assumptions:
• Total amount to be divided = Rs 25,000. • Ratio A : B : C = 1/10 : 1/6 : 1/15. • We must compute C's share in rupees.

Concept / Approach:
As with other fractional ratio problems, we first clear the denominators by multiplying each term by a suitable common multiple. This converts the fractional ratio into a simpler whole-number ratio. Once we have that, we proceed as usual: we consider the total sum as being split into a number of equal parts equal to the sum of the ratio terms, and we then assign the correct number of parts to each person. This process turns the problem into a routine ratio distribution task.

Step-by-Step Solution:
Step 1: The given ratio is 1/10 : 1/6 : 1/15. Step 2: Determine the least common multiple of the denominators 10, 6 and 15. The least common multiple is 30. Step 3: Multiply each term of the ratio by 30 to convert to whole numbers: A term: (1/10) * 30 = 3. B term: (1/6) * 30 = 5. C term: (1/15) * 30 = 2. Step 4: So the simplified whole-number ratio is A : B : C = 3 : 5 : 2. Step 5: Total parts = 3 + 5 + 2 = 10. Step 6: The value of one part = Total amount / Total parts = 25,000 / 10 = 2,500. Step 7: C's share corresponds to 2 parts. So C's share = 2 * 2,500 = 5,000.

Verification / Alternative Check:
We can also compute A and B's shares to verify. A's share = 3 * 2,500 = 7,500. B's share = 5 * 2,500 = 12,500. Total of shares = 7,500 + 12,500 + 5,000 = 25,000, which matches the original amount. Furthermore, the ratio 7,500 : 12,500 : 5,000 simplifies by dividing all three by 2,500, giving 3 : 5 : 2, which matches the simplified ratio derived from the fractional terms. This confirms that C's share is correct.

Why Other Options Are Wrong:
• 7,500 and 12,500 correspond to A and B's shares, not C's. • 10,000 would correspond to four parts of 2,500 and breaks the 3 : 5 : 2 ratio.

Common Pitfalls:
Some students mistakenly treat 1/10, 1/6 and 1/15 as direct weights without clearing denominators, leading to inconsistent calculations. Others incorrectly add the fractions instead of converting them into a whole-number ratio. Always multiply each fractional term by the least common multiple of denominators first, simplify the ratio, and then distribute the total amount accordingly.

Final Answer:
C receives Rs 5,000 out of Rs 25,000.