A cistern can be filled by two pipes in 20 and 30 minutes respectively. Both pipes being opened, when the first pipe must be turned off so that the cistern may be filled in 10 minutes more.

Explanation:-

% Cistern is filled by 1^st pipe in one minute = $$\frac{{100}}{{20}}$$ = 5%;
% Cistern is filled by 2^nd pipe in one minute = $$\frac{{100}}{{30}}$$ = 3.33%;
% cistern filled by 1^st and 2^nd pipes in one minute = 8.33%;

According to question,
Cistern is totally filled by 2^nd pipe in last 10 minute.
That means 2^nd pipe filled 33.3% of the cistern in last 10 minute and 66.66% of cistern is filled by 1^st and 2^nd pipe together in = $$\frac{{66.66}}{{8.33}}$$   = 8 minutes;
Thus, after 8 minute, 1^st pipe must be turned off.