Marks in the Sixth Subject: Step-by-Step Calculation

The question asks us to find the marks obtained by a student in the sixth subject, given the marks in five subjects and the average marks across all six subjects.

We are given:

• Marks in the first five subjects: 91, 86, 81, 79, and 92.
• Total number of subjects: 6.
• Average marks in all six subjects: 85.

The formula for calculating the average is:

\(\text{Average} = \frac{\text{Sum of observations}}{\text{Number of observations}}\)

In this case, the observations are the marks in the subjects. Let the marks in the sixth subject be denoted by \(x\).

The sum of marks in all six subjects will be the sum of the marks in the five known subjects plus the marks in the sixth subject:

\(\text{Sum of marks in 6 subjects} = 91 + 86 + 81 + 79 + 92 + x\)

First, let's calculate the sum of the marks in the five known subjects:

\(\text{Sum of marks in 5 subjects} = 91 + 86 + 81 + 79 + 92\)

\[91 + 86 = 177\]

\[177 + 81 = 258\]

\[258 + 79 = 337\]

\[337 + 92 = 429\]

So, the sum of marks in the five subjects is 429.

Now, we know the average of the six subjects is 85. Using the average formula:

\[85 = \frac{\text{Sum of marks in 6 subjects}}{6}\]

We can find the total sum of marks in all six subjects by rearranging the formula:

\(\text{Sum of marks in 6 subjects} = \text{Average} \times \text{Number of subjects}\)

\[\text{Sum of marks in 6 subjects} = 85 \times 6\]

\[85 \times 6 = 510\]

So, the total sum of marks in the six subjects is 510.

Now we have the relationship:

\(\text{Sum of marks in 6 subjects} = \text{Sum of marks in 5 subjects} + \text{Marks in the sixth subject}\)

\[510 = 429 + x\]

To find the value of \(x\), we subtract the sum of the marks in the five subjects from the total sum of marks in six subjects:

\[x = 510 - 429\]

\[x = 81\]

Therefore, the marks received in the sixth subject are 81.