Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick's age is $1$ year less than the average age of all three, then Harry's age, in years, is

In an examination, the average marks of $4$ girls and $6$ boys is $24$. Each of the girls has the same marks while each of the boys has the same marks. If the marks of any girl is at most double the marks of any boy, but not less than the marks of any boy, then the number of possible distinct integer values of the total marks of $2$ girls and $6$ boys is

The average of $30$ integers is $5$. Among these $30$ integers, there are exactly $20$ which do not exceed $5$. What is the highest possible value of the average of these $20$ integers?

A CAT aspirant appears for a certain number of tests. His average score increases by $1$ if the first $10$ tests are not considered, and decreases by $1$ if the last $10$ tests are not considered. If his average scores for the first $10$ and the last $10$ tests are $20$ and 30, respectively, then the total number of tests taken by him is

A batsman played $n + 2$ innings and got out on all occasions. His average score in these $n + 2$ innings was 29 runs and he scored 38 and 15 runs in the last two innings. The batsman scored less than 38 runs in each of the first $n$ innings. In these $n$ innings, his average score was 30 runs and lowest score was $x$ runs. The smallest possible value of $x$ is

Manu earns Rs. $4000$ per month and wants to save an average of Rs. $550$ per month in a year. In the first nine months, his monthly expense was Rs. $3500$, and he foresees that, tenth month onward, his monthly expense will increase to Rs. $3700$. In order to meet his yearly savings target, his monthly earnings, in rupees, from the tenth month onward should be

In a group of $10$ students, the mean of the lowest $9$ scores is $42$ while the mean of the highest $9$ scores is $47$. For the entire group of $10$ students, the maximum possible mean exceeds the minimum possible mean by