In a business partnership among P, Q, R and S, the profit is shared as follows:

$\frac{\text{P's share}}{\text{Q's share}} = \frac{2}{3}$, $\frac{\text{Q's share}}{\text{R's share}} = \frac{4}{5}$, $\frac{\text{R's share}}{\text{S's share}} = \frac{5}{12}$.

If the total profit is ₹24850, the difference (in ₹) of the combined share of profit of P and S and that of Q and R taken together is

Understanding what we need to find: We have 4 partners (P, Q, R, S) sharing profit in certain ratios. We need to find the difference between (P's share + S's share) vs (Q's share + R's share).

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Convert all ratios to a common form. The ratios are given separately, but we need one combined ratio to compare all four partners.

Given ratios:

$\dfrac{P}{Q} = \dfrac{2}{3}$; $\dfrac{Q}{R} = \dfrac{4}{5}$; $\dfrac{R}{S} = \dfrac{5}{12}$

By making the numbers the same, we get:

$P : Q : R : S = 8 : 12 : 15 : 36$

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Calculate individual shares:

Total ratio parts = $8 + 12 + 15 + 36 = 71$ parts

Since total profit = ₹$24,850$

Each part = $\dfrac{24850}{71} = ₹350$

Individual shares:

• P's share = $8 \times 350 = ₹2,800$
• Q's share = $12 \times 350 = ₹4,200$
• R's share = $15 \times 350 = ₹5,250$
• S's share = $36 \times 350 = ₹12,600$

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Find the required difference:

Combined share of P and S = $2,800 + 12,600 = ₹15,400$

Combined share of Q and R = $4,200 + 5,250 = ₹9,450$

Difference = $15,400 - 9,450 = ₹5,950$