Question 52

A batsman played n + 2 innings and got out on all occasions. HisĀ average score in these n + 2 innings was 29 runs and he scored 38 andĀ 15 runs in the last two innings. The batsman scored less than 38 runsĀ in each of the first n innings. In these n innings, his average score wasĀ 30 runs and lowest score was x runs. The smallest possible value of xĀ is

Solution

Given, $$\frac{\text{sum of scoresĀ in n matches+38+15}}{n+2}=29$$

Given,Ā $$\frac{\text{sum of scoresĀ in n matches}}{n}=30$$

=> 30n + 53 = 29(n+2) => n=5

Sum of the scores in 5 matches = 29*7 - 38-15 = 150

Since the batsmen scored less than 38, in each ofĀ the first 5 innings. The value of x will be minimum when remaining four values are highest

=> 37+37+37+37 + x = 150

=> x = 2

Video Solution

video

Create a FREE account and get:

  • All Quant CAT complete Formulas and shortcuts PDF
  • 35+ CAT previous year papers with video solutions PDF
  • 5000+ Topic-wise Previous year CAT Solved Questions for Free

Related Formulas With Tests

cracku

Boost your Prep!

Download App