Questions below followed by three quantities. Find the relationship between them. Quantity I: In a class with a certain number of students if a teacher weighing 78 kg is added, then average weight of class is increased by 2 kg. If one more teacher weighing 66 kg is added, then the average weight of the class increases by 3.5 kg over the original average. What is the original average weight (in kg) of the class Quantity II: The average age of 16 students and their teacher's age is 16 years. If the teacher's age is excluded, the average reduces by 2. What is the teacher's age Quantity III: Average weight of three friends A, B and C is 46 kg. Another person D joins the group and now the average is 45 kg. If another person E whose weight is 6 kg more than D, joins the group replacing A, then average weight of B, C, D and E becomes 47 kg. What is the weight of A (in kg)?

Option 3 : Quantity I < Quantity II > Quantity III

Let the students in a class be x

And average of class is y

According to question,

⇒ (xy + 78)/(x + 1) = y + 2

⇒ xy + 78 = xy + 2x + y + 2

⇒ 2x + y = 76     ---(i)

Now, another teacher joined the class

⇒ (xy + 78 + 66)/(x + 2) = y + 3.5

⇒ xy + 144 = xy + 3.5x + 2y + 7

⇒ 3.5x + 2y = 137     ---(ii)

By equation (I) and (II)

⇒ 0.5x = 15

⇒ x = 30

Original weight, y = 16 kg

Quantity II:

16S + T = 16 × 17

⇒ 16S + T = 272 years

After excluding the age of teacher average of 16 students is,

⇒ 16S = 14 × 16

⇒ 224 years

∴ teacher’s age = 272 - 224 = 48 years

Quantity III:

A + B + C = 46 × 3 = 138 kg

A + B + C + D = 45 × 4 = 180 kg     ---(i)

D = 180 - 138 = 42 kg

So, E = D + 6

E = 42 + 6 = 48 kg

Now,

B + C + D + E = 47 × 4 = 188 kg     ---(ii)

From equation (i) and (ii),

E - A = 188 - 180 = 8 kg

⇒ 48 - A = 8

⇒ A = 40 kg

Quantity I < Quantity II > Quantity III