To find the number of runs scored by R, we need to first understand the distribution ratio among the players P, Q, and R. The given ratios are:

• \(P : Q = 5 : 7\)
• \(Q : R = 2 : 3\)

Our task is to combine these two ratios into one common ratio for P, Q, and R. Let's do this step-by-step:

First, equate the common player Q's quantities in both ratios by finding a common multiple. For \(Q : R = 2 : 3\), multiply both sides of \(P : Q = 5 : 7\) by 2:

• \(P : Q = 5 \times 2 : 7 \times 2 = 10 : 14\)

Similarly, multiply both sides of \(Q : R = 2 : 3\) by 7 to match the Q part:

• \(Q : R = 2 \times 7 : 3 \times 7 = 14 : 21\)

Now combine both ratios as P : Q : R: \(10 : 14 : 21\).

The total sum of the parts is:

• \(10 + 14 + 21 = 45\)

Given that the total runs scored by P, Q, and R is 765, each part represents:

• \(1 \text{ part} = \frac{765}{45} = 17\)

Therefore, the runs scored by R (21 parts) is:

• \(21 \times 17 = 357\)

Hence, the number of runs scored by R is 357.