P, Q and R are three batsmen. The ratios of runs scored by them in a certain match were as follows:
P : Q = 5 : 7 and Q : R = 2 : 3.
If they scored a total of 765 runs, then find the number of runs scored by R.
357
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.
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