a) 20 min
b) 40 min
c) 60 min
d) 80 min
Answer: d
Explanation: Volume of cistern :
$$\eqalign{
& = \left( {\pi \times {{10}^2} \times 15} \right){m^3} \cr
& = 1500\pi {m^3} \cr} $$
Volume of water flowing through the pipe in 1 sec :
$$\eqalign{
& = \left( {\pi \times 0.25 \times 0.25 \times 5} \right){m^3} \cr
& = 0.3125\pi {m^3} \cr} $$
Time taken to fill the cistern :
$$\eqalign{
& = \left( {\frac{{1500\pi }}{{0.3125\pi }}} \right) \cr
& = \left( {\frac{{1500 \times 10000}}{{3125}}} \right) \cr
& = 4800\,\sec \cr
& = \left( {\frac{{4800}}{{60}}} \right)\min \cr
& = 80\,\min \cr} $$
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