There were 1,350 examinees in an examination. Out of them, 700 passed in Account, 600 passed in economics, 350 passed in Statistics and 50 failed in all three subjects. Moreover, 200 passed in economics and statistics, 150 students passed in ...

To find Abhishek Jain's average typing rate overall, we can use the formula: \[ \text{Average Rate} = \frac{\text{Total Pages Typed}}{\text{Total Time Spent Typing}} \] On Sunday, he typed 50 pages at the rate of 30 pages per hour. So, the time spent typing on Sunday is: \[ \text{Time on Sunday} = \Read more

To find Abhishek Jain’s average typing rate overall, we can use the formula:

\[

\text{Average Rate} = \frac{\text{Total Pages Typed}}{\text{Total Time Spent Typing}}

\]

On Sunday, he typed 50 pages at the rate of 30 pages per hour. So, the time spent typing on Sunday is:

\[

\text{Time on Sunday} = \frac{\text{Pages Typed}}{\text{Rate}} = \frac{50}{30} \text{ hours}

\]

On Monday, he typed 50 extra pages at the rate of 20 pages per hour. So, the time spent typing on Monday is:

\[

\text{Time on Monday} = \frac{\text{Pages Typed}}{\text{Rate}} = \frac{50}{20} \text{ hours}

\]

The total pages typed over both days is:

\[

\text{Total Pages Typed} = 50 + 50 = 100 \text{ pages}

\]

The total time spent typing is:

\[

\text{Total Time Spent Typing} = \text{Time on Sunday} + \text{Time on Monday} = \frac{50}{30} + \frac{50}{20} \text{ hours}

\]

Now, we can calculate the average rate:

\[

\text{Average Rate} = \frac{\text{Total Pages Typed}}{\text{Total Time Spent Typing}} = \frac{100}{\frac{50}{30} + \frac{50}{20}} \text{ pages per hour}

\]

\[

\text{Average Rate} = \frac{100}{\frac{5}{3} + \frac{5}{2}} = \frac{100}{\frac{10}{6} + \frac{15}{6}} = \frac{100}{\frac{25}{6}} = \frac{100 \times 6}{25} = \frac{600}{25} = 24 \text{ pages per hour}

\]

So, Abhishek Jain’s average typing rate overall is 24 pages per hour.

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### Given Data: - Total examinees = 1350 - Passed in Accounts (\(A\)) = 700 - Passed in Economics (\(E\)) = 600 - Passed in Statistics (\(S\)) = 350 - Failed in all subjects = 50 - Passed in Economics and Statistics (\(E \cap S\)) = 200 - Passed in Accounts and Statistics (\(A \cap S\)) = 150 - PassRead more

### Given Data:

– Total examinees = 1350

– Passed in Accounts (\(A\)) = 700

– Passed in Economics (\(E\)) = 600

– Passed in Statistics (\(S\)) = 350

– Failed in all subjects = 50

– Passed in Economics and Statistics (\(E \cap S\)) = 200

– Passed in Accounts and Statistics (\(A \cap S\)) = 150

– Passed in Statistics only = 50

### Calculations:

1. **Total Passed in at least one subject**:

\[

\text{Total passed} = 1350 – 50 = 1300

\]

2. **Using Venn Diagram and Principle of Inclusion-Exclusion**:

\[

|A \cup E \cup S| = |A| + |E| + |S| – |A \cap E| – |E \cap S| – |A \cap S| + |A \cap E \cap S|

\]

Let’s denote \( x = |A \cap E \cap S| \).

3. **Substitute given values**:

\[

1300 = 700 + 600 + 350 – |A \cap E| – 200 – 150 + x

\]

Simplify the equation:

\[

1300 = 1650 – |A \cap E| – 350 + x

\]

\[

1300 = 1300 – |A \cap E| + x

\]

\[

0 = – |A \cap E| + x

\]

\[

x = |A \cap E|

\]

To find \( |A \cap E| \):

4. **Determine students passing only Economics**:

From the image:

\[

\text{Students passing Economics only} = 600 – 200 – x = 450

\]

5. **Determine students passing only Accounts**:

From the image:

\[

\text{Students passing Accounts only} = 700 – 150 – x = 550

\]

### Correct Results:

1. **Passed in at least one subject**:

\[

1300

\]

2. **Passed in all three subjects**:

\[

50

\]

3. **Passed in Economics only**:

\[

450

\]

4. **Failed in Accounts**:

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1350 – 700 = 650

\]