Question

present age of mother of manish is 1 year more than 5 times the present age of manish.four years before if the products of their ages was 22 then find the present age of manish and his mother​

Answer 1

Answer:

age of Manish is 5 years

age of his mother is 26 years.

Step-by-step explanation:

see the attachment

Answer 2

Given that, Age of mother of manish is 1 year more than 5 times the present age of manish and hence before four years, The product of their ages was 22.

❍ So, Let's consider age of his son be x years.

⠀ ⠀Therefore, age of mother will be (5x + 1) years.

⠀━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀

☆ Before four years,

• Age of Son = (x - 4) years
• Age of mother = (5x + 3) years

⠀⠀⠀

$\begin{gathered}\qquad\bigstar\:{\underline{\pmb{\frak{\pink{According~to~the~Question~:}}}}}\\\\\\ \qquad\dashrightarrow\sf Mother's\:age = 5 \bigg(Son's\:age \bigg) + 1 \\\\\\ \qquad\dashrightarrow\sf (x - 4 ) (5x + 3 )= 22\\\\\\ \qquad\dashrightarrow\sf {5x}^{2} - 3x - 20x + 12 = 22\\\\\\ \qquad\dashrightarrow\sf {5x}^{2} - 23x + 12 = 22\\\\\\ \qquad\dashrightarrow\sf {5x}^{2} - 23x + 12 - 22=0\\\\\\ \qquad\dashrightarrow\sf{5x}^{2} - 25x + 2x- 10=0\\\\\\ \qquad\dashrightarrow\sf 5x(x - 5) + 2(x - 5)\\\\\\ \qquad\dashrightarrow\sf(x - 5)(5 + 2)\\\\\\ \qquad\dashrightarrow{\underline{\boxed{\pmb{\frak{x = 5}}}}}\:\bigstar\\\\\end{gathered}$

Therefore,

⠀⠀⠀

• Age of Son, x = 5 years
• Age of his mother = (5x + 1) i.e 5(5) + 1 = 26 years

⠀⠀⠀

$\therefore\:{\underline{\sf{Hence,\:Present\:Age\:of\:mother\:\&\:his\:son\:is\:{\pmb{26}\:\sf{and}\: \pmb{5\:years}}}\:\sf{respectively.}}}$