Question

10 years ago the average age of a family of 4membersr was 24, in the meantime, two children born by a gap of two yrs, what is the age of younger child if the average age family is same as it was 10 years ago.

Answer 1

THANKS FOR THE QUESTION !

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ANS :

........................ 3 YRS ......................

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GIVEN :

=> 10 YRS AGO :

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NO. OF FAMILY MEMBERS :

=> 4

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AVERAGE OF AGES :.

=> 24 YRS

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10 YRS AGO :

=> THE SUM OF AGES OF ALL FAMILY MEMBERS :

=> NO. OF MEMBERS * AVERAGE

=> 4 * 24

=> 96

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AT PRESENT :

=> THE SUM OF AGES OF 4 FAMILY MEMBERS :

=> 10 * NO. OF MEMBERS + PREVIOUS SUM

=> 10 * 4 + 96 YRS

=> 40 + 96 YRS

=> 136 YRS

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CONDITION :

=> IN BETWEEN GAP :

=> 2 BABIES BORN BY A GAP OF 2 YRS

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TOTAL FAMILY MEMBERS NOW ,

=> 4 + 2

=> 6

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STILL THE AVERAGE IS SAME :

=> AS PER THE AVERAGE BEFORE 10 YRS

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SUM OF AGES OF ALL FAMILY MEMBERS NOW,

=> NO. OF MEMBERS * AVERAGE

=> 6 * 24 YRS

=> 144 YRS

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TO FIND :

=> AGE OF SMALLER CHILD

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SUM OF AGES OF 2 CHILDREN :

=> SUM OF AGES OF ALL 6 FAMILY MEMBERS - SUM OF AGES OF 4 FAMILY MEMBERS

=> 144 - 136

=> 8 YRS

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LET,

=> THE AGE OF THE SMALLER CHILD BE :

=> X

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2 YRS AGO BIGGER CHILD WAS BORN :

=> SO, AGE OF BIGGER CHILD :

=> X + 2 YRS

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BUT THE SUM OF AGES OF 2 CHILDREN :

=> 8 YRS

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ACCORDING TO INFO :

=> X + X + 2 YRS = 8 YRS

=> 2X + 2 YRS = 8 YRS

=> 2X YRS. = 8 YRS - 2 YRS

=> 2X YRS = 6 YRS

=> X YRS = 6 / 2 YRS

=> X = 3 YRS

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SO,

=> THE AGE OF YOUNGER CHILD IS X YRS

=> MEANS

=> ...................... 3 YRS ........................

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HOPE IT WILL HELP U ......

THANKS AGAIN.........

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Answer 2

Answer:  The required age of the younger child is 3 years.

Step-by-step explanation:  Given that 10 years ago, the average age of a family of 4 members was 24. In the meantime, two children born by a gap of two yrs.

We are to find the age of the younger child if the average age of the family is same as it was 10 years ago.

Let x years be the age of the younger child and let S be the sum of the ages of the members of the family before 10 years.

Then, according to the given information, we have

$\dfrac{S}{4}=24\\\\\Rightarrow S=96~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Therefore, the present average age of the family is given by

$\dfrac{S+4\times10+x+x+2}{6}=24\\\\\\\Rightarrow S+40+2x+2=144\\\\\Rightarrow 96+40+2x+2=144~~~~~~~~~~~~~~~~~~~~~[\textup{Using (i)}]\\\\\Rightarrow 2x+138=144\\\\\Rightarrow 2x=144-138\\\\\Rightarrow 2x=6\\\\\Rightarrow x=\dfrac{6}{2}\\\\\Rightarrow x=3.$.

Thus, the required age of the younger child is 3 years.