   Directions: Study the following questions carefully and answer the questions given below.
Important for :
1
The average of 15 numbers is 7. If the average of the first 8 numbers be 6.5 and the average of last 8 numbers be 9.5, then the middle number is
» Explain it
C
As per the given information, we get

Average of 15 numbers = 7. So, total of the numbers = 15 × 7 = 105

Average of first 8 numbers = 6.5. So, total of the numbers = 8 × 6.5 = 52

Average of last 8 numbers = 9.5. So, total of the numbers = 8 × 9.5 = 76

Hence, the 8th number = (52 + 76) – 105 = 128 – 105 = 23.

Hence, option C is correct.

2
If a, b, c, d, e are five consecutive odd numbers, their average is
» Explain it
D
Numbers:
a, b  = (a + 2), c = (a + 4), d = (a + 6), e = (a + 8)

 ∴    Required avg = a + a + 2 + a + 4 + a + 6 + a + 8 = 5a + 20 5 5

 ⇒ 5(a + 4) = a + 4. 5

Hence, option D is correct.

3
The average mathematics marks of two sections A and B of class IX in the annual examination is 74. The average marks of Section A is 77.5 and that of section B is 70. The ratio of the number of students of section A and B is
» Explain it
C
Let the number of students in section A is x and B is y, then

 74 = 77.5 × x + 70 × y x + y

⇒ 74x + 74y = 77.5x + 70y

 ⇒  4y = 3.5x   ⇒ x = 4 = 8 y 3.5 7

⇒   8 : 7.

Hence, option C is correct.

4
In a certain year, the average monthly income of a person was Rs. 3400. For the first eight months of the year, his average monthly income was Rs. 3160 and for the last five months , it was Rs. 4,120. His income in the eighth month of the year was:
» Explain it
B
As per the given information, we get

Average of 12 months = 3400. So, total salary of all 12 months = 3400 × 12 = ₹ 40800            (eq. 1)

Average of first 8 months = 3160. So, total salary of first 8 months = 3160 × 8 = ₹ 25280          (eq. 2)

Average of last 5 months = 4120. So, total salary of first 5 months = 4120 × 5 = ₹ 20,600         (eq. 3)

Person's income in the eighth month = (25280 + 20600) – 40800 = 45880 – 40800 = ₹ 5080.

Note: In such questions, when we calculate total of two different sets (for instance, first 8 months + last 5 months), one particular value (8th month in this case) is calculated twice.

On subtracting the total of eq. 1 from the total of eq. 2 and 3 we are left with the value of the month that's been calculated twice in the question.

Hence, option B is correct.

5
Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 56, then difference of the first and third number is
» Explain it
D
Let the numbers are 2x, x, 4x, then,

Total of the numbers = 3 × 56 = 168

⇒    2x + x + 4x = 168

⇒    7x = 168 ⇒ x = 24

∴     Required difference = 4x – 2x = (4 × 24) – (2 × 24)

⇒ 96 – 48 = 48.

Hence, option D is correct.