Question

Find the product of the age of Virat before 7 years and after 7 years is 480. Find his present age.

Answer 1

Hint: The idea or method to solve such a question is the formation of equations from the given data set information. Such questions also include the conditions which will be very helpful in forming the equations. Consider the unknown quantity as any variable and proceed with the solution.

Complete step-by-step answer:
$ * $ If Before is given or ago is given = Use sign.
$ * $ If After is given = Use sign.
Step by Step Solution:
(Step 1) Let the age of Virat at present be x years.
 Age of Virat seven years ago =$(x - 7)$ years.
(Step 2) Age of Virat seven years after = $(x + 7)$ years.
(Steps 3) Given the product of the age of Virat before and after seven years is 480. So just write down the equations formed from the given conditions.
Age of Virat seven years ago $ \times $ Age of Virat after seven years = $480$
Just substitute the values in the above equation then we get,
$
  (x - 7) \times (x + 7) = 480 \\
  {x^2} + 7x - 7x - 49 = 480 \\
  {x^2} - 49 = 480 \\
  {x^2} = 529 \\
  x = \pm \sqrt {529} \\
  x = \pm 23years \\
 $
(Step 4) We have two answers one with a positive sign and the other with a negative sign. But we know that age cannot be a negative value and so our final answer is positive and includes value x.

Final answer: The present age of Virat after computed from the given data is 23 years.

Note: You can simply speed up your calculation by simply multiply $(x + 7)$ and $(x - 7)$ which will eventually take the form of $(a + b)$ and $(a - b)$ which will give $({a^2} - {b^2})$ as the answer. So in the same way instead of multiplying one by one we will get directly ${x^2} - 49$ as equal to $480$. After solving from here we will get the same answer as we get above.