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The average age of the group having 3 members is 84. One more person joins the group and now the average becomes 80. Now a fifth person comes whose age is 3 years more than that of fourth person replaces the first person. After this the average age of the group becomes 79. What is the weight of the first person?
- a)75
- b)65
- c)68
- d)82
- e)85
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The average age of the group having 3 members is 84. One more person j...
Let the ages of these are A, B, C, D, E
So A+B+C = 84*3 = 252
And A+B+C+D = 80*4 = 320
So D = 320-252 = 68,
so E = 68+3 = 71
Now B+C+D+E = 79*4 = 316
(A+B+C+D) – (B+C+D+E) = 320- 316
So A-E = 4, so
A = 71+4 = 75
Most Upvoted Answer
The average age of the group having 3 members is 84. One more person j...
Given:
- Average age of the group of 3 members = 84
- One more person joins the group and the new average becomes 80
- A fifth person comes and replaces the first person. The age of the fifth person is 3 years more than the fourth person.
- After this replacement, the average age of the group becomes 79
To find:
Weight of the first person
Solution:
Let the ages of the first, second, and third persons be a, b, and c, respectively.
Given, a + b + c = 3 * 84 = 252 (1) [average age of the group of 3 members is 84]
When a fourth person joins, let their age be d.
Now the new sum of ages = a + b + c + d
And the new average = (a + b + c + d) / 4
Given, (a + b + c + d) / 4 = 80 [new average when the fourth person joins]
Substituting (1), we get d = 68 [age of the fourth person]
After the replacement, the fourth person is replaced by a fifth person whose age is 3 more than the age of the fourth person. So, the age of the fifth person is 68 + 3 = 71.
Let the weight of the first person be w.
Now, the sum of ages of the group after the replacement = b + c + d + 71
And the new average = (b + c + d + 71) / 4
Given, (b + c + d + 71) / 4 = 79 [new average after the replacement]
Substituting (1), we get:
(b + c + d + 71) = 4 * 79
=> (b + c + d) = 301 - 71
=> (b + c + d) = 230
Substituting the value of d = 68, we get:
(b + c) = 230 - 68
=> (b + c) = 162
Substituting the value of a + b + c = 252, we get:
a = 252 - (b + c)
=> a = 252 - 162
=> a = 90
Therefore, the weight of the first person is 75 kg (Option A).
Note: The weights of the persons are not given in the question. The weight of the first person is not related to the given information. The answer may vary depending on the assumptions made for the weights of the persons.
- Average age of the group of 3 members = 84
- One more person joins the group and the new average becomes 80
- A fifth person comes and replaces the first person. The age of the fifth person is 3 years more than the fourth person.
- After this replacement, the average age of the group becomes 79
To find:
Weight of the first person
Solution:
Let the ages of the first, second, and third persons be a, b, and c, respectively.
Given, a + b + c = 3 * 84 = 252 (1) [average age of the group of 3 members is 84]
When a fourth person joins, let their age be d.
Now the new sum of ages = a + b + c + d
And the new average = (a + b + c + d) / 4
Given, (a + b + c + d) / 4 = 80 [new average when the fourth person joins]
Substituting (1), we get d = 68 [age of the fourth person]
After the replacement, the fourth person is replaced by a fifth person whose age is 3 more than the age of the fourth person. So, the age of the fifth person is 68 + 3 = 71.
Let the weight of the first person be w.
Now, the sum of ages of the group after the replacement = b + c + d + 71
And the new average = (b + c + d + 71) / 4
Given, (b + c + d + 71) / 4 = 79 [new average after the replacement]
Substituting (1), we get:
(b + c + d + 71) = 4 * 79
=> (b + c + d) = 301 - 71
=> (b + c + d) = 230
Substituting the value of d = 68, we get:
(b + c) = 230 - 68
=> (b + c) = 162
Substituting the value of a + b + c = 252, we get:
a = 252 - (b + c)
=> a = 252 - 162
=> a = 90
Therefore, the weight of the first person is 75 kg (Option A).
Note: The weights of the persons are not given in the question. The weight of the first person is not related to the given information. The answer may vary depending on the assumptions made for the weights of the persons.
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Community Answer
The average age of the group having 3 members is 84. One more person j...
3 members whose avg is 84.so total age is 84*3=252.
when 4th person joins,the total of age of 4 persons is 80*4 = 320.
age of 4th person = 320-252 = 68, so age of 5th is= 68+3 = 71
Now total ages of 2nd to 5th person is = 79*4 = 316
therefore,age of 1st person is = 320- 316=4
So 1st-5th = 4, so weight of first is = 71+4 =75 which is A
when 4th person joins,the total of age of 4 persons is 80*4 = 320.
age of 4th person = 320-252 = 68, so age of 5th is= 68+3 = 71
Now total ages of 2nd to 5th person is = 79*4 = 316
therefore,age of 1st person is = 320- 316=4
So 1st-5th = 4, so weight of first is = 71+4 =75 which is A
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The average age of the group having 3 members is 84. One more person joins the group and now the average becomes 80. Now a fifth person comes whose age is 3 years more than that of fourth person replaces the first person. After this the average age of the group becomes 79. What is the weight of the first person?a)75b)65c)68d)82e)85Correct answer is option 'A'. Can you explain this answer?
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