In three unit tests of Mathematics Priyal got 75,82 and 90 marks. How many marks must she obtain in Unit test IV to have an average of 85 in the four unit tests?

Answer

To find out how many marks Priyal must obtain in Unit Test IV to achieve an average of 85 across four unit tests, we can follow these steps:

### Step 1: Understand the average formula
The average of a set of numbers is calculated by dividing the sum of the numbers by the total count of the numbers. In this case, we want the average of four unit tests.

### Step 2: Set up the equation
Let the marks Priyal needs in Unit Test IV be denoted as \( x \). The marks she received in the first three tests are 75, 82, and 90. The formula for the average is:
\[ \text{Average} = \frac{\text{Sum of all marks}}{\text{Number of tests}} \]
For Priyal, we want:
\[ 85 = \frac{75 + 82 + 90 + x}{4} \]

### Step 3: Calculate the total marks needed for the average
To find the total marks needed for an average of 85 over four tests, we can rearrange the equation:
\[ 85 \times 4 = 75 + 82 + 90 + x \]
Calculating the left side:
\[ 340 = 75 + 82 + 90 + x \]

### Step 4: Calculate the sum of the first three tests
Now, we calculate the sum of the marks Priyal received in the first three tests:
\[ 75 + 82 + 90 = 247 \]

### Step 5: Substitute the sum back into the equation
Now, substitute the sum back into the equation:
\[ 340 = 247 + x \]

### Step 6: Solve for \( x \)
To find \( x \), we subtract 247 from both sides:
\[ x = 340 - 247 \]
Calculating the right side gives:
\[ x = 93 \]

### Conclusion
Priyal must obtain **93 marks** in Unit Test IV to achieve an average of 85 across all four tests.

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