The average weight of $45$ students in a class was calculated as $36 \,kg$. It was later found that the weight of two students in the class was wrongly calculated. The actual weight of one of the boys in the class was $32 \,kg ,$ but it was calculated as $34$ $kg ,$ and the weight of another boy in the class was $45 \,kg ,$ whereas it was calculated as $40 \,kg$. What is the actual average weight of the $45$ students in the class ? (in $kg$) (Rounded off to two-digits after decimal)
$36.07$
$36.16$
$35.84$
Cannot be determind
In a set of prime and composite numbers, the composite numbers are twice the number of prime number and the average of all the numbers of the set is $9 .$ If the number of prime numbers and composite numbers are exchanged then the average of the set of numbers is increased by $2 .$ If during the exchange of the numbers the average of the prime numbers and composite numbers individually remained constant, then the ratio of the average of composite numbers to the average of prime numbers (initially) was
If the average of $x$ and $\frac{1}{x}(x \neq 0)$ is $M,$ then the average of $x^{2}$ and $\frac{1}{x^{2}}$ is
The average of marks obtained by $150$ candidates in a certain examination is $50 .$ If the average marks of passed candidates is $55$ and that of the failed candidates is $25,$ what is the number of candidates who passed the examination?
A cricketer scored some runs in his continuous $9$ innings. He scored $100$ runs in his $10^{th}$ innings and this increased his average by $8$ runs. What was the average of his runs at the end of $10^{th}$ innings?
The average age of Donald, his wife and their two children is $23\, years.$ His wife is just $4 \,year$ younger than Donald himself andxhis wife was $24\, years$ old when his daughter was born. He was $32 \,years$ old when his son was born. Th average age of Donald and his daughter is ? (in $year$)