The average marks of 3 students A, B and C are 48. Another student D joins the group and the new average becomes 44 marks. If yet another student E, who has 3 marks more than D, joins the group, the average of the 4 students B, C, D and E becomes 43 marks. Find the marks scored by A.
Solution: The first sentence g ives a total of 144 for A’s, B’s and C’s marks. Second sentence: When D joins the group, the total becomes 44 4 = 176. Hence, D must get 32 marks. Alternatively, you can reach this point by considering the first two statements together as: D’s joining the group reduces the average from 48 to 44 marks (i.e. 4 marks). This means that to maintain the average of 48 marks, D has to take 4 marks from A, 4 from B and 4 from C or A, i.e. a total of 12 marks. Hence, he must have got 32 marks. From here: The first part of the third sentence gives us information about E getting 3 marks more than 32. Hence, E gets 35 marks. Now, it is further stated that when E replaces A, the average marks of the students reduce by 1, to 43. Mathematically, this can be shown as A + B + C + D = 44 × 4 = 176 B + C + D + E = 43 × 4 = 172 Subtracting the two equations, we get A – E = 4 marks. Hence, A would have got 39 marks. Alternatively, you can think of this as: The replacement of A with E results in the reduction of 1 mark from each of the 4 people who belong to the group. Hence, the difference is 4 marks. Hence, A would get 4 marks more than E, i.e. 39 marks.