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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Important Questions from Ratio and proportion
A’s marks in Mathematics are directly proportional to practice time. In 6 hours of practice, A gets 70 marks. What should be the practice time (approximately) to get 90 marks?
The average of the areas of 2 similar triangles is 706.5 m2 whose perimeters are in the ratio of 6 : 11. What is 20% of the difference (in m2) in areas of both triangles?
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In a triangle ABC, P and Q are two points on AB and AC, respectively, such that PQ is parallel to BC. If AC = 5QC, then the ratio PQ : BC is equal to:
Find the mean proportional between 25 and 81.
