A new student of weight 45 kg came in place of old student due to whic

1.	A new student of weight 45 kg came in place of old student due to which the average weight of 20 students in the class increased by 1.5 kg. What was the weight of old student?1. 30 kg2. 15 kg3. 20 kg4. 40 kg
Answer» Correct Answer - Option 2 : 15 kg Given: A new student of weight 45 kg came in place of the old student. The average weight of 20 students in the class increased by 1.5 kg. Concepts used: Average weight = (Total weight of all students)/(Number of students) Calculation: Let the original average weight of students be x kg. Original total weight of all students = 20 × x = 20x The average weight of 20 students in the class increased by 1.5 kg. So, New average weight = x + 1.5 kg A new student of weight 45 kg came in place of the old student. Let the weight of the old student be y kg. New total weight of 20 students = Original total weight of all students + Weight of new student – weight of old student ⇒ New total weight of 20 students = 20x + 45 – y New average weight = x + 1.5 kg Average weight = Total weight of all students/Number of students ⇒ x + 1.5 = (20x + 45 – y)/20 ⇒ 20 × (x + 1.5) = 20x + 45 – y ⇒ 20x + 30 = 20x + 45 – y ⇒ y = 45 – 30 kg = 15 kg ∴ The weight of old student was 15 kg.

A new student of weight 45 kg came in place of old student due to which the average weight of 20 students in the class increased by 1.5 kg. What was the weight of old student?1. 30 kg2. 15 kg3. 20 kg4. 40 kg

Answer» Correct Answer - Option 2 : 15 kg

Given:

A new student of weight 45 kg came in place of the old student. The average weight of 20 students in the class increased by 1.5 kg.

Concepts used:

Average weight = (Total weight of all students)/(Number of students)

Calculation:

Let the original average weight of students be x kg.

Original total weight of all students = 20 × x = 20x

The average weight of 20 students in the class increased by 1.5 kg.

So, New average weight = x + 1.5 kg

A new student of weight 45 kg came in place of the old student.

Let the weight of the old student be y kg.

New total weight of 20 students = Original total weight of all students + Weight of new student – weight of old student

⇒ New total weight of 20 students = 20x + 45 – y

New average weight = x + 1.5 kg

Average weight = Total weight of all students/Number of students

⇒ x + 1.5 = (20x + 45 – y)/20

⇒ 20 × (x + 1.5) = 20x + 45 – y

⇒ 20x + 30 = 20x + 45 – y

⇒ y = 45 – 30 kg = 15 kg

∴ The weight of old student was 15 kg.