Question

The mean score of a person is 30 in 'n'
exams. If he would have scored six
marks extra in each of the first (n-1)
exams, his mean score would have
been 35. Find the number of exams.​

Answer 1

Answer:

Average = total score / number of tests

total score = 180 + 150 = 330

50% average = 330 * 0.5 = 165 ( he needs to score this )

He has scored 30% in the first test with 180 marks

so he has already scored 0.3 * 180 = 54

Now He needs to score 165-54 = 111 in the second test.

So the precentage = 111/150 = 74

( 0.74 * 150 = 74 * 1.5 = 74 + 74/2 = 74 + 37 = 111 )

Answer 2

Answer:

n = 6.

Step-by-step explanation:

Given

• Mean of mean of scores in 'n' exams is = 30
• he scored 6 marks more in each of the (n -1) exams.

to find

• number of exams held.

Approach

• mean is = 30

• the total number of score in 'n' exams is equal to 35n.

Equation Formed

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: 30n + 6(n - 1) = 35n$

Simplify both sides of the equation:-

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: 30n +( 6)(n) + (6)( - 1) = 35n$

Combine like terms:-

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: (30n + 6n) + ( - 6) = 35n$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: \: 36n - 6 = 35n$

Subtract 35n from both sides:-

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: 36n - 6 - 35n = 35n - 35$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: n - 6 = 0$

Add 6 to both sides:-

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: n - 6 + 6 = 0 + 6$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \sf \: n = 0$