The average weight of a group of members increased from 28 kg to 32 kg

1.	The average weight of a group of members increased from 28 kg to 32 kg, when three new members of weight 32 kg, 34 kg and 46 kg join the group. Find the initial number of members in the group.1. 42. 53. 64. 75. 8
Answer» Correct Answer - Option 1 : 4 Given: Initial average of the group = 28 kg Final average after three members were included = 32 kg Weights of members included in the group = 32 kg, 34 kg and 46 kg Formula used: Average = Sum of observations/ Number of observations Calculation: Let the number of members initially in the group be x Initial sum of observations = (28 × x) Total number of observations when three new members joined the group ⇒ [(28 × x) + (32 + 34 + 46)] Total number of members in the group after three members were added ⇒ (x + 3) According to Question, [(28 × x) + (32 + 34 + 46)]/(x + 3) = 32 ⇒ [28x + 112]/(x + 3) = 32 ⇒ [28x + 112] = 32 × (x + 3) ⇒ 28x + 112 = 32x + 96 ⇒ 112 – 96 = 32x – 28x ⇒ 16 = 4x ⇒ x = 4 ∴ The initial number of members in a group is 4.

The average weight of a group of members increased from 28 kg to 32 kg, when three new members of weight 32 kg, 34 kg and 46 kg join the group. Find the initial number of members in the group.1. 42. 53. 64. 75. 8

Answer» Correct Answer - Option 1 : 4

Given:

Initial average of the group = 28 kg

Final average after three members were included = 32 kg

Weights of members included in the group = 32 kg, 34 kg and 46 kg

Formula used:

Average = Sum of observations/ Number of observations

Calculation:

Let the number of members initially in the group be x

Initial sum of observations = (28 × x)

Total number of observations when three new members joined the group

⇒ [(28 × x) + (32 + 34 + 46)]

Total number of members in the group after three members were added

⇒ (x + 3)

According to Question,

[(28 × x) + (32 + 34 + 46)]/(x + 3) = 32

⇒ [28x + 112]/(x + 3) = 32

⇒ [28x + 112] = 32 × (x + 3)

⇒ 28x + 112 = 32x + 96

⇒ 112 – 96 = 32x – 28x

⇒ 16 = 4x

⇒ x = 4

∴ The initial number of members in a group is 4.