Q.A and B are partners whose capitals are in the ratio $5:7$. If B's share of the annual profit is $4900$ rupees, find the total profit and A's share.

Because profit is shared in the ratio of capitals, B's share is $7$ of the $12$ parts, which fixes the value of one part and hence the whole profit.

The capitals are in the ratio $5 : 7$, so — this being a simple partnership — the profit is shared in the same ratio $5 : 7$. The total number of parts is $5 + 7 = 12$, and B receives the $7$-part share.

Step 1 — value of one part from B's share. B's share corresponds to $7$ parts and equals $4900$ rupees, so $\text{one part} = \frac{4900}{7} = 700 \text{ rupees}.$

Step 2 — total profit. The total profit is all $12$ parts: $\text{Total profit} = 12 \times 700 = 8400 \text{ rupees}.$

Step 3 — A's share. A receives $5$ parts: $A = 5 \times 700 = 3500 \text{ rupees}.$ …

Alternatively, using B's share as a fraction of the total: B gets $\frac{7}{12}$ of the profit $P$, so $\frac{7}{12}P = 4900 \Rightarrow P = \frac{4900\times 12}{ …

A common slip is to divide B's share by the total number of parts $12$ instead of by B's own number of parts $7$ — the value of one part must be found fro …