P6 Math: Student average mark

 A group of students sat for a test. Their average mark was 74.5. Three students found out that their marks were wrongly recorded as 63 instead of 84. The mark increased to 76.3 after correcting the mistakes.

(a) How many students sat for the test?

(b) A student who was absent sat for the test when he came back to school. The average mark decreased to 75 when his marks was included. What was the total marks the class scored?

Solution:

I am one of the fan to solve average problems using basic definition of average itself i.e average is total mark divide by number of students. Later, apply simple algebra and understanding of the problem variation to solve.

Take a look into this problem:

We have two equations:

(1)  74.5 = T/n, where T represents total mark and n is number of students

(2) After correction is made, 76.3 = (T + 21 + 21 + 21)/n. There are three students with correction.

Combine (1) and (2):

(1) T = 74.5n

(2) (T + 63) = 76.3n

1.8n = 63 --> n = 35 --> total students = 35

In second problem, the total students = 35 + 1 = 36

So total marks of the class will be = 76 x 36 = 2736