Question 1169855
A cistern can be filled by two pipes. The small pipe alone will take 24 minutes 
longer than the larger pipe to fill the cistern alone. The small pipe alone will take 32 minutes longer to fill the cistern alone than when the two pipes are operating together. How long will it take the larger pipe to fill the cistern alone
<pre>Let time it takes large pipe to fill cistern, be L
Then, large pipe can to fill {{{1/L}}} of cistern, in 1 minute
Also, time it takes small pipe to fill cistern = L + 24
Thus, small pipe can fill {{{1/(L + 24)}}} of cistern in 1 minute 
In addition, time taken by both to fill cistern: L + 24 - 32, or L - 8
Therefore, both pipes can fill {{{1/(L - 8)}}} of cistern in 1 minute 

       We then get: {{{matrix(1,3, 1/L + 1/(L + 24), "=", 1/(L  -  8))}}}
(L + 24)(L  -  8) + L(L  -  8) = L(L + 24) -------- Multiplying by LCD, L(L + 24)(L - 8)
{{{matrix(3,3, L^2 + 16L  -  192 + L^2  -  8L, "=", L^2 + 24L, L^2 + L^2  -  L^2 + 16L  -  8L - 24L  -  192, "=", 0, L^2 - 16L  -  192, "=", 0)}}}
               (L - 24)(L + 8) = 0
Time it takes larger pipe to fill cistern, or {{{highlight_green(matrix(1,4, L, "=", 24, minutes))}}}           OR            L  = - 8 (ignore)

You can do the CHECK!!</pre>