A batsman played three matches in a tournament. The respective ratio between the scores of 1st and 2nd match was 8 : 9 and that between the scores of 2nd and 3rd match was 3 : 2. The difference between the 1st and 3rd match was 16 runs. What was the batsman’s average score in all the three matches ?
Ratio between the scores of 1st and 2nd match was 8 : 9
Let score in 1st match = $$8x$$
=> Score in 2nd match = $$9x$$
Also, ratio between the scores of 2nd and 3rd match was 3 : 2
=> Score in 3rd match = $$6x$$
Acc. to ques, => $$8x - 6x = 16$$
=> $$x = \frac{16}{2} = 8$$
Total runs in the three matches = $$8x + 9x + 6x = 23x$$
= $$23 \times 8 = 184$$
$$\therefore$$ Required average = $$\frac{184}{3} = 61 \frac{1}{3}$$
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