The average weight of 20 contestants in a fashion show increased by 5.

1.	The average weight of 20 contestants in a fashion show increased by 5.75 kg when one of the contestants left the show but when a new contestant joined the show then the average weight decreased by 2.75 kg. What is the difference between the weight of the new contestant who joined the show and the contestant who left the show?1. 55.5 kg2. 49.75 kg3. 51.5 kg4. Cannot be determined5. None of the above
Answer» Correct Answer - Option 3 : 51.5 kg Calculation: Let the average weight of the 20 contestants be x kg Total weight = 20x kg Let the weight of the contestant who left the show be y kg ∴ According to the question: ⇒ 20x – y = (x + 5.75) × 19 ⇒ x = 109.25 + y ----(i) Again, when one of the new contestants joined the show then let the weight of the new contestant who joined the class be z kg ⇒ 20x + z = (x – 2.75) × 21 ⇒ z = x – 57.75 ----(ii) Putting the value of x from equation (i) in equation (ii), ⇒ z = 109.25 + y – 57.75 ∴ the required difference = z – y ⇒ 51.5 kg The difference between the age of the new contestant who joined the show and the contestant who left the show is 51.5 kg.

The average weight of 20 contestants in a fashion show increased by 5.75 kg when one of the contestants left the show but when a new contestant joined the show then the average weight decreased by 2.75 kg. What is the difference between the weight of the new contestant who joined the show and the contestant who left the show?1. 55.5 kg2. 49.75 kg3. 51.5 kg4. Cannot be determined5. None of the above

Answer» Correct Answer - Option 3 : 51.5 kg

Calculation:

Let the average weight of the 20 contestants be x kg

Total weight = 20x kg

Let the weight of the contestant who left the show be y kg

∴ According to the question:

⇒ 20x – y = (x + 5.75) × 19

⇒ x = 109.25 + y ----(i)

Again, when one of the new contestants joined the show then let the weight of the new contestant who joined the class be z kg

⇒ 20x + z = (x – 2.75) × 21

⇒ z = x – 57.75 ----(ii)

Putting the value of x from equation (i) in equation (ii),

⇒ z = 109.25 + y – 57.75

∴ the required difference = z – y

⇒ 51.5 kg

The difference between the age of the new contestant who joined the show and the contestant who left the show is 51.5 kg.