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 April 11th, 2018, 09:12 PM #1 Senior Member   Joined: Aug 2014 From: India Posts: 310 Thanks: 1 The present average age of.... The present average age of a family of five members is 29 years. If the present age of the youngest member in the family is five years, then what was the average age of the family at the time of the birth of the youngest member {Ans is 30} I tried: Average of five members is $\displaystyle \frac {X}{5} = 29$. $\displaystyle \frac {(29\times5)-5}{4}$ $\displaystyle 5\times\frac {28}{4}$ = $\displaystyle 35$. Where I am doing wrong? Last edited by Ganesh Ujwal; April 11th, 2018 at 09:14 PM.
 April 12th, 2018, 03:44 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 The problem is that your "Ans= 30" is wrong! If "If the present age of the youngest member in the family is five years" then the "the time of the birth of the youngest member" was five years ago. Every one in the family was 5 years younger then, not one year older! If the average age of everyone in the family is now 29, 5 years ago, it was 24.
 April 12th, 2018, 03:58 AM #3 Global Moderator   Joined: Dec 2006 Posts: 19,511 Thanks: 1743 Immediately after the birth of the youngest member, the average age of all five was 29 - 5 = 24, so their ages totalled 24 × 5 = 120. The youngest's age was zero, so the average age of the other four was 120/4 = 30. If the answer is to be 30, "the time of the birth of the youngest member" must refer to immediately before that youngest member is counted as a member of the family.
April 12th, 2018, 04:34 AM   #4
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 Originally Posted by Ganesh Ujwal $\displaystyle \frac {(29\times5)-5}{4}$ $\displaystyle 5\times\frac {28}{4}$ = $\displaystyle 35$. Where I am doing wrong?
Each member of the family was five years younger five years ago, so you should subtract $5 \times 5$ from the present sum of their ages.

Alternatively, the average age of the five family members was five years less five years ago, so the average of the four eldest then was$$(29-5)\frac54=30$$

In all your questions here, I see a general pattern of attempting to do everything in a single step. (See Find the age of A 5 years hence. and What is the average of all the odd natural numbers upto 51?) As a result, you confuse yourself. You should work in smaller steps and at each stage understand exactly what the quantities you have actually mean.

Last edited by v8archie; April 12th, 2018 at 04:47 AM.

April 12th, 2018, 06:16 AM   #5
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Quote:
 Originally Posted by Ganesh Ujwal Where I am doing wrong?
Your work was arguably correct, if you completed it by subtracting 5 from your answer of 35 to obtain 30.

April 12th, 2018, 07:30 AM   #6
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 Originally Posted by skipjack Your work was arguably correct, ....
Everybody here is so ready to hate me except you.

April 12th, 2018, 08:49 AM   #7
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 Originally Posted by Ganesh Ujwal Everybody here is so ready to hate me except you.
Why do you believe that if someone points out errors in your thinking, then that person hates you?

Nothing that v8archie or Country Boy has said is hateful in any way.

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