a) 3 hrs 15 min
b) 3 hrs 45 min
c) 4 hrs
d) 4 hrs 15 min
Answer: b
Explanation: Time taken by one tap to fill half of the the tank = 3 hours
Part filled by the four taps in 1 hour
$$\eqalign{
& = {4 \times \frac{1}{6}} = \frac{2}{3} \cr
& {\text{Remaining}}\,{\text{part}} = {1 – \frac{1}{2}} = \frac{1}{2} \cr
& \frac{2}{3}:\frac{1}{2}::1:x \cr
& \Rightarrow x = {\frac{1}{2} \times 1 \times \frac{3}{2}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{3}{4}\,hrs.\,\,i.e.,\,45\,\operatorname{mins} . \cr
& {\text{So,}}\,{\text{total}}\,{\text{time}}\,{\text{taken}} = 3\,hrs.\,45\,mins. \cr} $$
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