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Question

The weighted average marks of 170 students who appeared in an exam is 55. It is also known that the average marks of failed students is 23 and that of passed students is 63. Find the number of students who passed the exam.

A
34
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B
62
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C
106
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D
136
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Solution

The correct option is D 136
The formula to calculate the weighted average is,

Weighted Average=(w1×n1)+(w2×n2)++(wl×nl)w1+w2++wl,

where w1,w2,wl are the weighted factors and n1,n2,nl are the data points.

Let the number of failed students be x, then the number of passed students will be 170x.

Thus, the given information will be depicted as,


Here, the weighted factors are the number of students with w1=x and w2=170x and their corresponding average marks are the data points denoted by n1=23 and n2=63.

It is given that the weighted average marks is 55 and the total number of students is 170, i.e., w1+w2=170.

Substitute the required values in the formula of weighted average to calculate the value of x.

55=(x×23)+((170x)×63)17055×170=23x+1071063x9350=1071040x40x=107109350x=136040x=34

Thus, the number of failed students is x=34 and the number of passed students is calculated as,

Passed students=170x=136

Hence, 136 students passed the exam.

So, option (d) is correct.

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