Question 990633
Let total runs scored before = x
No of innings = y
Avg. = x/y
After scoring 21,
Avg. = (x+21)/(y+1) which should be equal to (x/y) + 1
or, {{{(x+21)/(y+1) = (x/y) + 1 }}}
=> {{{y(x+21) = (y+1)*(x+y)}}}
=> {{{xy + 21y = xy + y^2 + x + y}}}
=> {{{y^2 - 20y + x = 0 }}} ------------------------(i)
Similarly,
{{{(x+21+35)/(y+2) = (x/y) + 3}}}
=> {{{yx + 56y = xy + 2x + 3y^2 + 6y}}}
=> {{{3y^2 - 50y + 2x = 0}}} -----------------------(ii)
Multiplying (i) by 2, we get,
{{{2y^2 - 40y + 2x = 0 }}} ------------------------(iii)
Subtracting (iii) from (ii)
{{{y^2 -10y = 0}}}
=> y = 10 (Since y can not be 0)
Putting in (i)
100-200 + x = 0
=>  x = 100
So runs scored including 21 and 35  = 100 +21 +35 = 156