Question 760546
Sohan's age is 7 more than a square number.

So, if x is the age,

{{{x = n^2 + 7}}} for some number n.

Next number = n+1

x is also given to be 6 less than the next square number.

i.e. {{{x = (n+1)^2 - 6}}}

Equating the two values of x,

{{{n^2 + 7 = (n+1)^2 - 6}}}

Expanding (n+1)^2

{{{n^2 + 7 = n^2 + 2*n + 1 - 6 = n^2 + 2*n - 5}}}

Removing n^2 from both sides

{{{7 = 2*n - 5}}}

i.e

{{{2*n = 12}}}

i.e.

{{{n = 6}}}

So Sohan's age is {{{6^2 + 7 = 43}}} years.

In how many years will Sohan be 80 years old?

Sohan will be 80 in another {{{80 - 43 = 37}}} years.