Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?

Explanation:-

$$\eqalign{ & {\text{Let their investments be}}\, \cr & Rs.\,x\,{\text{for}}\,{\text{14}}\,{\text{months}},\, \cr & Rs.\,y\,{\text{for}}\,{\text{8}}\,{\text{months}}\,{\text{and}}\, \cr & Rs.\,z\,{\text{for}}\,{\text{7}}\,{\text{months}}\,{\text{respectively}}. \cr & {\text{Then}},\,14x:8y:7z = 5:7:8 \cr & {\text{Now}},\frac{{14x}}{{8y}} = \frac{5}{7} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,98x = 40y \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,y = \frac{{49}}{{20}}x \cr & {\text{And}},\frac{{14x}}{{7z}} = \frac{5}{8} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,112x = 35z \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,z = \frac{{112}}{{32}}x = \frac{{16}}{5}x \cr & \therefore x:y:z \cr & = x:\frac{{49}}{{20}}x:\frac{{16}}{5}x \cr & = 20:49:64 \cr}$$