The average marks of 30 students in mathematics is 69. If the class leader’s mark is included then the average becomes 70. Find the class leader’s mark.
69 = Σx/30
70 = Σx/31
Solve each for Σx, then subtract one from the other.
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To find the class leader's mark, we can use the concept of averages. Let's break down the problem step by step:
Step 1: Find the sum of the marks of all 30 students.
The average marks of 30 students is given as 69. Therefore, the sum of their marks can be calculated by multiplying the average (69) by the number of students (30): 69 * 30 = 2070.
Step 2: Find the sum of the marks including the class leader's mark.
The average marks, when the class leader's mark is included, becomes 70. Since there are now 31 students, multiply the new average (70) by the total number of students (31): 70 * 31 = 2170.
Step 3: Find the class leader's mark.
To find the class leader's mark, subtract the sum of the marks of 30 students from the sum of the marks including the class leader's mark: 2170 - 2070 = 100.
Therefore, the class leader's mark is 100.