a) $$1\frac{{13}}{{17}}$$ hours
b) $$2\frac{8}{{11}}$$ hours
c) $$3\frac{9}{{17}}$$ hours
d) $$4\frac{1}{2}$$ hours
Answer: c
Explanation:
$$\eqalign{
& {\text{Net}}\,{\text{part}}\,{\text{filled}}\,{\text{in}}\,{\text{1}}\,{\text{hour}} \cr
& = {\frac{1}{5} + \frac{1}{6} – \frac{1}{{12}}} = \frac{{17}}{{60}} \cr
& {\text{The}}\,{\text{tank}}\,{\text{will}}\,{\text{be}}\,{\text{full}}\,{\text{in}}\,\frac{{60}}{{17}}\,{\text{hours}} \cr
& i.e.,\,3\frac{9}{{17}}\,{\text{hours}} \cr} $$
Difference between their ages
$$\eqalign{
& = \left( {8x – 7x} \right) \cr
& = {\text{ }}x\,{\text{years}} \cr
& {\text{ = 2}}\,{\text{years}} \cr} $$
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