A sum of Rs. 53 is divided among A, B and C in such a way that A gets Rs. 7 more than what B gets and B gets Rs. 8 more than what C gets. The ratio of their share is gets. The ratio of their share is = ?

Explanation:-

$$\eqalign{ & {\text{Let C gets }}x{\text{ rupees}} \cr & \therefore {\text{B gets }}x + 8{\text{ rupees}} \cr & \therefore {\text{A gets }}x + 8 + 7{\text{ rupees}} \cr & {\text{Total A}} + {\text{B}} + {\text{C}} \cr & \Rightarrow x + 15 + x + 8 + x = 3x + 23 \cr & \Rightarrow 3x + 23 = {\text{Rs}}{\text{. }}53({\text{given)}} \cr & \Rightarrow 3x = 30 \cr & \Rightarrow x = 10 \cr & \Rightarrow x = {\text{Rs}}{\text{.10}} \cr & \therefore {\text{Ratio of their shares is }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{A}}\,\,\,\,\,\,\,\,\,:\,\,\,\,\,\,{\text{B}}\,\,\,\,\,\,\,\,:\,\,\,{\text{C}} \cr & {\text{ = }}\left( {x + 15} \right):\left( {x + 8} \right):\left( x \right) \cr & = \,\,\,\,\,\,\,\,\,25\,\,\,\,\,\,\,\,\,:\,\,\,\,\,\,\,18\,\,\,\,\,:\,\,10 \cr}$$