Average age of a group of 8 persons was 14 years a person with age 28 year left the group and a new person with age 16 year join the group find the new average age of the group.
Answers
Step-by-step explanation:
Correct option is C)
r of persons be n
Given that the average age of n number of people is 16 years
Therefore, 16=nsum of the ages of n people
⟹sum of the ages of n people=16n -------(1)
Given that the average of the 20 new people is 15 years
Therefore, 15=20sum of the ages of 20 new people
⟹sum of the ages of 20 new people=300 -------(2)
Given that after adding 20 new persons the total average becomes 15.5 years
Therefore, 15.5=20+nsum of the ages of n people + sum of the ages of the 20 new people
⟹sum of the ages of n people + sum of the ages of the 20 new people=15.5(20+n) -------(3)
substituting (1) and (2) in (3) we get
16n+300=310+15.5n
⟹16n−15.5n=310−300
⟹0.5n=10
⟹n=20
Therefore number of persons initially going for the picnic is 20
Answer:
Question
The average age of a number of persons in a group was calculated as 35 years, which was 2.5 years more than the correct average as there was an error in recording the age to two persons as 38.5 years and 40 years instead of 29 years and 22 years respectively. The number of persons in the group was:
This question was previously asked in
SSC CGL Previous Paper 70 (Held On: 4 March 2020 Shift 3)
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15
12
11
13
Answer (Detailed Solution Below)
Option 3 : 11
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Detailed Solution
Let the number of persons in the group be x, then
Wrong average of age of persons in the group = 35
Wrong sum of age of person in the group = 35x
Correct average of age of persons in the group = 35 – 2.5 = 32.5
Correct sum of age of persons in the group = 32.5x
According to the question
35x – 32.5x = 38.5 + 40 – 29 – 22
⇒ 2.5x = 27.5
⇒ x = 27.5/2.5
⇒ x = 11
Short Trick:
Total number of persons in the group = (38.5 + 40 – 29 – 22)/2.5 =11
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