finding outliers and counting number of occurrence

Here's a dplyr solution:

raw_data %>% 
  mutate(salary_flag =
           ifelse(salary > 15000, 1, 0),
         expenditure_flag = ifelse(expenditure > 10000, 1, 0)) %>% 
  group_by(id) %>% 
  mutate(total_outlier = sum(salary_flag) + sum(expenditure_flag))

You are flagging for salary and expenditure, then grouping by id and calculating the sum of all salary_flag and the sum of all expenditure_flag for each id.

 id salary expenditure salary_flag expenditure_flag total_outlier
  <int>  <dbl>       <dbl>       <dbl>            <dbl>         <dbl>
1     1  10000       10000           0                0             0
2     2  15000       15000           0                1             1
3     3  20000       20000           1                1             2
4     4  40000       30000           1                1             2
5     5  50000       40000           1                1             2

If you're only concerned with the total outliers, @MartinGal provided a very nice option:

raw_data %>% 
group_by(id) %>% 
mutate(total_outlier = sum(salary>15000, expenditure>10000))

Gives us:

     id salary expenditure total_outlier
  <int>  <dbl>       <dbl>         <int>
1     1  10000       10000             0
2     2  15000       15000             1
3     3  20000       20000             2
4     4  40000       30000             2
5     5  50000       40000             2

edit:

This seems to get the end result that you're looking for:

raw_data %>% 
  group_by(id) %>% 
  summarise(count = sum(salary>15000, expenditure>10000),
            value = min(salary)) %>% 
  mutate(title = "salary") %>% 
  select(id, title, value, count)

Which gives you:

     id title  value count
  <int> <chr>  <dbl> <int>
1     1 salary 10000     0
2     2 salary 15000     1
3     3 salary 20000     2
4     4 salary 40000     2
5     5 salary 50000     2

You can try the following

raw_data <- data.frame("id" = 1:5, 
                       "salary" = c(10000,15000,20000,40000,50000), 
                       "expenditure" = c(10000,15000,20000,30000,40000))

raw_data$SaleryOutlier <- ifelse(
    raw_data$salary > 15000, TRUE, FALSE)

raw_data$ExpenditureOutlier <- ifelse(
    raw_data$expenditure > 10000, TRUE, FALSE)

You can then use aggregate function to summarize the data, e.g. for each id by using FUN=sum. This should look like

aggregate(raw_data, by=list(id = raw_data$id), FUN=sum)

This works because TRUE=1.

I hope this helps.

EDIT

Based on your comment, I guess you are looking for

raw_data <- data.frame("id" = c(1, 1, 1, 2, 2), 
                       "salary" = c(10000,15000,20000,40000,50000), 
                       "expenditure" = c(10000,15000,20000,30000,40000))

raw_data$SaleryOutlier <- ifelse(
  raw_data$salary > 15000, TRUE, FALSE)

raw_data$ExpenditureOutlier <- ifelse(
  raw_data$expenditure > 10000, TRUE, FALSE)

raw_data_aggregate <- aggregate(raw_data, by=list(id = raw_data$id), FUN=sum)

raw_data_aggregate$count <- raw_data_aggregate$SaleryOutlier + raw_data_aggregate$ExpenditureOutlier

EDIT TWO

If you want to aggregate over two variables, just exchange the above aggregate with

raw_data_aggregate <- aggregate(
  SalaryOutlier + ExpenditureOutlier ~ id + salary + expenditure, raw_data, FUN=sum)

EDIT THREE

Based on the comments below, I created the following code

raw_data <- data.frame(
  "id" = c(1, 1, 1, 2, 2),
  "salary" = c(10000,15000,20000,40000,50000),
  "expenditure" = c(10000,15000,20000,30000,40000))

# Identify salary outliers
raw_data$SalaryOutlier <- ifelse(
  raw_data$salary > 15000, TRUE, FALSE)

# Identify expenditure outliers
raw_data$ExpenditureOutlier <- ifelse(
  raw_data$expenditure > 10000, TRUE, FALSE)

# Aggregate over id + salay
raw_data_aggregate_salary <- aggregate(
  SalaryOutlier ~ id + salary, raw_data, FUN=sum)

# Aggregate over id + expenditure
raw_data_aggregate_expenditure <- aggregate(
  ExpenditureOutlier ~ id + expenditure, raw_data, FUN=sum)

# Just some renaming to fit with desired output data frame.
raw_data_aggregate_salary$question_name <- "salary"
raw_data_aggregate_expenditure$question_name <- "expenditure"

colnames(raw_data_aggregate_salary)[2] <- "values"
colnames(raw_data_aggregate_expenditure)[2] <- "values"

colnames(raw_data_aggregate_salary)[3] <- "count"
colnames(raw_data_aggregate_expenditure)[3] <- "count"

# Bind result together into one df.
raw_data_aggregate <- rbind(
  raw_data_aggregate_salary, raw_data_aggregate_expenditure)

# Only select entries where we actually have a count.
raw_data_aggregate <- subset(
  raw_data_aggregate,
  raw_data_aggregate$count > 0)

# Order to fit with desired output
raw_data_aggregate <- raw_data_aggregate[ order(raw_data_aggregate$id), ]

Raw data is :

    raw_data <- data.frame("id" = c(1, 1, 1, 2, 2), 
                           "salary" = c(10000,15000,20000,40000,50000), 
                           "expenditure" = c(10000,15000,15000,30000,40000))

And the solution is :

    raw_data <- raw_data %>% filter(salary>15000 | expenditure>10000)
    entry_variables <- raw_data %>%select(id,salary,expenditure) %>% 
      pivot_longer(cols = -id,
                   names_to = "Question_name", values_to= "Value", 
                   values_drop_na = TRUE) %>%
      count(id, Question_name, Value)

In a data.table this would look like

raw_data[, flag0 := (salary > 15000) + (expenditure > 10000)]
raw_data[, flag := sum(flag0), by = "id"]

Here flag0 is the flag by row (which can later be deleted if you like) and flag would be the final result.

Edit: Seeing your reply to @Matt, you seem to want the total amount by salary and expenditure seperately. You can do something like

raw_data[, flag_salary := as.integer(salary > 15000)]
raw_data[, flag_expenditure := as.integer(expenditure > 10000)]
raw_data[, flag_salary := sum(flag_salary), by = "id"]
raw_data[, flag_expenditure := sum(flag_expenditure), by = "id"]