A, B, and C are partners in a Business. A and B are sharing the ratio in 3:4 and B: C are sharing in 5:9. At the end of the year, the profit received is Rs 71000. What is the share of A?
Rs. 15000
The two given ratios are \(A : B = 3 : 4\) and \(B : C = 5 : 9\). To combine them, the value of B must be made equal in both.
The B-terms are 4 and 5; their LCM is 20. Scale the first ratio by 5: \(A : B = 15 : 20\). Scale the second by 4: \(B : C = 20 : 36\).
Now B matches, so the combined ratio is \(A : B : C = 15 : 20 : 36\).
The total number of parts is \(15 + 20 + 36 = 71\).
The profit Rs. 71,000 is split over 71 parts, so one part equals \(\dfrac{71000}{71} = 1000\).
A's share is 15 parts: \(15 \times 1000 = 15000\). Key concept: chain two ratios by equalising the common term before dividing the total in that proportion.
Hence the share of A is Rs. 15000.
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