The average age of the mother and her six children is 12 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother

Answer: Option D

Explanation:

Let the average after 17th match is x
then the average before 17th match is x-3

so 16(x-3) + 87 = 17x
=> x = 87 - 48 = 39

Answer: Option B

Explanation:

As the month begin with sunday, so there will be five sundays in the month. So result will be:
\begin{aligned}
= (\frac{510 \times 5 + 240 \times 25}{30})
= (\frac{8550}{30}) = 285
\end{aligned}

Answer: Option C

Explanation:

Let the average weight of the 59 students be A.
So the total weight of the 59 of them will be 59*A.

The questions states that when the weight of this student who left is added, the total weight of the class = 59A + 45
When this student is also included, the average weight decreases by 0.2 kgs

\begin{aligned}
\frac{59A + 45}{60} = A - 0.2
\end{aligned}

=> 59A + 45 = 60A - 12
=> 45 + 12 = 60A - 59A
=> A = 57

Answer: Option D

Explanation:

Prime numbers between 30 and 50 are:
31, 37, 41, 43, 47

Average of prime numbers between 30 to 50 will be
\begin{aligned}
(\frac{31+37+41+43+47}{5}) = \frac{199}{5} = 39.8
\end{aligned}

Answer: Option D

Explanation:

Suppose total number of students are = X
\begin{aligned}
Total increase = x*\frac{1}{2} = \frac{x}{2} \\
=> \frac{x}{2} = 83-63 = 20 \\
=> x = 40
\end{aligned}