Math, asked by janilpandya, 11 months ago



4. Four years ago, a father's age was square of
his daughter's age. Nine years hence, his age
will be 2 more than thrice his daughter's age.
Find their present ages.

Answers

Answered by taliyah2
6

Answer:

27 and 9

Step-by-step explanation:

Answered by Anonymous
23

GIVEN :

  • Four years ago father's age was square of his daughter's age.

  • Nine years later his age will be 2 more than thrice than his daughter's age.

TO FIND :

  • Their present age i.e., Father's and his daughter's age.

SOLUTION :

Let his daughter's age is x years.

4 years ago i.e., (x - 4) years

Squaring his father's age :

= (x - 4)²

Again,

  • It is told that Nine years later his age will be 2 more than thrice of his daughter's age.

So,

his daughter's age after 9 years : (x + 9) years.

Hence,

His father's age after 9 years :

= 2 + 3(x + 9) years

= 2 + 3x + 27

= 3x + 29 years

Which will be equal to (x - 4)² + 9 + 4

As it is total 13 years later.

According to the question,

  \bf \implies \: 3x + 29 = (x - 4)² + 9 + 4  \\

\bf \implies \:  3x + 29 =  {x}^{2} + 16 - 8x + 13 \\

\bf \implies \: 3x + 2 9=  {x}^{2}  - 8x + 29 \\

 \bf \implies \: 3x + 8x + 29 - 29 =  {x}^{2}   \\

 \bf \implies \:  {x}^{2}  = 11x \\

  \bf \implies \:  {x}^{2}  - 11x = 0 \\

\bf \implies \: x(x - 11) = 0 \\

\bf \implies \: x  -  11 = 0 \\

 \bold \gray \dag{ \underline{ \boxed{\orange {\bf  \therefore \: x = 11years. \blue\checkmark }}}}  \bold \gray \dag

HENCE,

His father's age is x = 11 years.

Her father's age is (x - 4)² + 4

\implies \bf (11 - 4)² + 4

\implies\bf  7² + 4

\implies \bf 49 + 4

\implies \bf 53 years.

  \purple \bigstar{ \underline{ \boxed{ \bf {\blue{ \: Required \: \blue  { answer : }}}}}} \purple \bigstar

 \bold \gray \dag{ \underline{ \boxed{ \bf { \orange { \therefore fathers \: age \:  = 53 years. \:  \blue \checkmark}}}}} \bold \gray \dag

\bold \gray \dag{ \underline{ \boxed{ \bf { \green { \therefore daughters \: age \:  = 11 years. \:  \red \checkmark}}}}} \bold \gray \dag

Verification :

  • Verification needs the L. H. S. = R. H. S. by substituting the value of x.

In the equation :

  \bf \implies \: 3x + 29 = (x - 4)² + 9 + 4  \\

 \bf \implies \: (3 \times 11) + 29 =  {(11 - 4) }^{2} + 13 \\

  \bf \implies \: 33 + 29 =  {7}^{2}  + 13 \\

 \bold \gray \dag { \underline{ \boxed{ \green{\bf \therefore\: 62 = 62 \:  \red \checkmark}}}} \bold \gray \dag

FINALLY,

L. H. S. = R. H. S.

{\underline{\boxed{ \green{\bf Hence,\purple   V \red e \orange r \pink i \blue f  \green i \red e \pink d  \red \checkmark }}}}

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