The average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs. 5200. What is the monthly income of A?

**Answer: **C

Let monthly income of A = a

monthly income of B = b

monthly income of C = c

\(a + b = 2 \times 5050~\cdots(Equation 1)\\ b + c = 2 \times 6250 ~\cdots(Equation 2)\\ a + c = 2 \times 5200 ~\cdots (Equation 3)\\ (Equation 1) + (Equation 3) - (Equation 2)\\ \Rightarrow a + b + a + c - (b + c) = (2 \times 5050) + (2 \times 5200) - (2 \times 6250)\\ \Rightarrow 2a = 2(5050 + 5200 - 6250)\\ \Rightarrow a = 4000\)

i.e., Monthly income of A = 4000

A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:

**Answer: **D

Since the month begins with a Sunday, to there will be five Sundays in the month.

Required average

\(\left( \dfrac {510 \times 5 + 240 \times 25}{30} \right)\\
=\dfrac{8550}{30}\\
=285\)

If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is:

**Answer: **B

Required average

\(\left( \dfrac {55 \times 50 + 60 \times 55 + 45 \times 60}{55+60+45} \right)\\
=\left( \dfrac {2750 + 3300 + 2700}{160} \right)\\
=\dfrac{8750}{160}\\
=54.68\)

A batsman makes a score of 87 runs in the 17th match and thus increases his average by 3. Find his average after 17th match.

**Answer: **D

Let the average after 17th match is \(x\)

Then the average before 17th match is \(x-3\)

So,

\(16(x-3) + 87 = 17x\\
\Rightarrow x = 87 - 48 = 39\)

A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 30 days starting with Sunday is:

**Answer: **B

As the month begin with Sunday, so there will be five Sundays in the month. So result will be:

\(= \left (\dfrac{510 \times 5 + 240 \times 25}{30}\right)\\
= \left( \dfrac{8550}{30} \right)\\
= 285\)

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