Step-by-step explanation:
Distance between two villages = d
[tex](a) \: \frac{4}{5} \: of \: d = \frac{4}{5} d \\ \\ (b) \: \frac{3}{4} \: of \: d = \frac{3}{4} d \\ \\ (c) \: \frac{4}{5} d - \frac{3}{4} d = 1.5 \\ \\ \therefore \: \bigg(\frac{4}{5} - \frac{3}{4} \bigg) d = 1.5 \\ \\ \therefore \: \bigg(\frac{4 \times 4 - 3 \times 5}{5 \times 4} \bigg) d = 1.5 \\ \\ \therefore \: \bigg(\frac{16- 15}{20} \bigg) d = 1.5 \\ \\ \therefore \: \bigg(\frac{1}{20} \bigg) d = 1.5 \\ \\ \therefore \: d = 1.5 \times 20 \\ \\ \: \: \: \: \: \huge \orange{ \boxed{{ \therefore \: d = 30}}}[/tex]
