Divide Rs. 1,18,000 among three persons A, B and C such that the ratio of A's share to B's share is 3 : 4 and the ratio of B's share to C's share is 5 : 6. What are the respective shares of A, B and C?

Introduction / Context:
This is a ratio based division problem where a total sum is to be divided among three persons according to two linked ratios. The ratios connect A with B and B with C, and from these we must determine a single combined ratio for A : B : C and then compute their actual monetary shares from the given total amount.

Given Data / Assumptions:

• Total amount to be divided among A, B and C is Rs. 1,18,000.
• Ratio of A's share to B's share is A : B = 3 : 4.
• Ratio of B's share to C's share is B : C = 5 : 6.
• We must find actual shares of A, B and C in rupees.

Concept / Approach:
We need a single combined ratio A : B : C that is consistent with both given ratios. To do this, we express A : B and B : C in such a way that the B term is the same in both ratios. Once a combined ratio is obtained, we treat it as a set of parts of the total amount. By dividing the total by the sum of the parts, we obtain the value of one part and then each person's share.

Step-by-Step Solution:
Step 1: Given A : B = 3 : 4, let A = 3x and B = 4x. Step 2: Given B : C = 5 : 6, let B = 5y and C = 6y. Step 3: Since B is common in both descriptions, we equate the two expressions for B. That is, 4x = 5y. Step 4: To make the B term equal in both ratios, choose a common value. One simple way is to take x = 5 and y = 4 so that 4x = 4 * 5 = 20 and 5y = 5 * 4 = 20. Step 5: With x = 5, A = 3x = 15 and B = 4x = 20. With y = 4, C = 6y = 24. Step 6: Therefore, the combined ratio A : B : C is 15 : 20 : 24. Step 7: Sum of the ratio parts is 15 + 20 + 24 = 59. Step 8: Total amount is Rs. 1,18,000. So one part is 118000 / 59. Step 9: Calculate 118000 / 59 = 2000. So each part is worth Rs. 2000. Step 10: A's share is 15 * 2000 = Rs. 30,000. Step 11: B's share is 20 * 2000 = Rs. 40,000. Step 12: C's share is 24 * 2000 = Rs. 48,000.

Verification / Alternative check:
Check that the shares satisfy the original ratios and sum to the total. First, A : B = 30000 : 40000 = 3 : 4 as required. Second, B : C = 40000 : 48000 = 5 : 6, which matches the second given ratio. Finally, 30000 + 40000 + 48000 = 118000, which equals the total amount. All conditions are satisfied, so the computed shares are correct.

Why Other Options Are Wrong:
The alternative options either assign a larger amount to A than to C or change the internal ratios incorrectly. For instance, in option A, A = 48000, B = 40000 and C = 30000, the ratio A : B becomes 6 : 5 instead of 3 : 4, and B : C becomes 4 : 3 instead of 5 : 6. Similarly, the other options do not simultaneously satisfy both given ratios. Only option B preserves both ratios correctly and sums to Rs. 1,18,000.

Common Pitfalls:
A frequent mistake is to add the ratios 3 : 4 and 5 : 6 directly or to average them instead of constructing a combined ratio through a common middle term. Some learners also forget to check whether the final shares obey both ratios. Always align the common term (here B), find the combined ratio, and only then apply it to the total amount.

Final Answer:
The correct division is A = Rs. 30,000, B = Rs. 40,000 and C = Rs. 48,000, which corresponds to option B.