Average weight of a group of some people increased by 1.5 kg if a person whose weight is 56 kg joined the group and the average weight increased by 2 kg if two persons whose average weight is 51 kg impectively joined the group. Find the number of people in the group initially.
Answers
Answer:
answer is 12
Step-by-step explanation:
people be x
avg=sum of all weight/number of people
atq
(avg+1.5=sum of all +56/x)=(avg+2=sum of all+51)
after solving
0.5x=6
Answer:
11
Step-by-step explanation:
let initial number of people = b
initial total weight of people = a kg
Initial average weight = x kg
Case Initial
a/b = x
= a = bx
Case1
56 kg person added and average increased by 1.5Kg
(a+56)/(b+1) = x+ 1.5
using a =bx
(bx+56)= (x+1.5)(b+1)
bx + 56 = bx + 1.5b + x + 1.5
56 = 1.5 b + x + 1.5
54.5 = 1.5 b + x. - (1)
Case 2
2 person with average weight 51kg was added and average increase by 2 Kg
weight of two person added = Average × No of people
= 51 × 2 = 102 kg
A.T.Q
(a+102)/(b+2) = x +2
using a = bx
(bx + 102) = (x +2)(b+2)
bx + 102 = bx + 2b + 2x +4
102 = 2b + 2x + 4
dividing both sides by 2
51 = b + x + 2
49 = b + x - (2)
from (1) & (2)
we get
b = 11
initial number of people = 11
x= 38kg
initial average weight = 38 kg
a = 418 kg
initial total weight = 418kg