Question

the sum of ages of father and daughter is 52 years. six years ago, the product of their ages were 175 find their present ages​

Answer 1

Father = 41 years old.

Daughter = 11 years old.

Explanation:

Let the present age of father and daughter be f and d respectively.

by condition given,

f + d = 52 - - -(i)

6 years ago, father and daughter were

f - 6 and d - 6 respectively.

By given condition,

(f - 6) × (d - 6) = 175 - - (ii)

From (i) d = 52 - f

substituting d = 52 - f in equation (ii), we get,

(f - 6) × (52 - f - 6) = 175

=> (f - 6) × (46 - f ) = 175

=>

${f}^{2} - 52f + 276 \: = - 175 \\ => {f}^{2} - 52f + 451 = 0$

${f}^{2} - 41f - 11f + 451 = 0 \\ => \: f(f - 41) - 11(f - 41)) = 0 \\ => (f - 11)(f - 41) = 0 \\ => f = 11 \: \: or \: \: \: \:f = \: \: 41$

(Since, father's age cannot be 11, therefore, rejecting f = 11)

Hence, father's present age = 41 years and

daughter's present age = 11 years.

Answer 2

Father = 41 years old.

Daughter = 11 years old.

Explanation:

Let the present age of father and daughter be f and d respectively.

by condition given,

f + d = 52 - - -(i)

6 years ago, father and daughter were

f - 6 and d - 6 respectively.

By given condition,

(f - 6) × (d - 6) = 175 - - (ii)

From (i) d = 52 - f

substituting d = 52 - f in equation (ii), we get,

(f - 6) × (52 - f - 6) = 175

=> (f - 6) × (46 - f ) = 175

=>

\begin{gathered} {f}^{2} - 52f + 276 \: = - 175 \\ = > {f}^{2} - 52f + 451 = 0\end{gathered}f2−52f+276=−175=>f2−52f+451=0

\begin{gathered} {f}^{2} - 41f - 11f + 451 = 0 \\ = > \: f(f - 41) - 11(f - 41)) = 0 \\ = > (f - 11)(f - 41) = 0 \\ = > f = 11 \: \: or \: \: \: \:f = \: \: 41\end{gathered}f2−41f−11f+451=0=>f(f−41)−11(f−41))=0=>(f−11)(f−41)=0=>f=11orf=41

(Since, father's age cannot be 11, therefore, rejecting f = 11)

Hence, father's present age = 41 years and

daughter's present age = 11 years.