Mr.	:	Mrs.
Before	7x	:	8x
After	5y	:	6y

Before 7x + 8x = 120

⇒ 15x = 120

⇒ x = 8

∴ Mr. Gupta = 7 $\times$ 8 = 56

Mrs. Gupta = 8 $\times$ 8 = 64

∴ After losing 6kg by Mr. Gupta the ratio be comes 5 : 6

⇒ Let Mrs. Gupta loss x kg \begin{align} & \therefore \frac{{56 - 6}}{{64 - x}} \times \frac{5}{6} \cr & \left( {{\text{Cross multiplication}}} \right) \cr\end{align} ⇒ 300 = 320 - 5x

⇒ 5x = 20

∴ x = 4 kg

\begin{align} & \Rightarrow {\text{A}}:{\text{B}}:{\text{C}} \cr & \, \, \, \, \, \, \, \, \, 2:5:4{\text{ }} \cr & 2x + 5x + 4x = 11x \cr & \Rightarrow 11x = {\text{Rs}}.126.50 \cr & \Rightarrow x = {\text{Rs}}{\text{.11}}{\text{.50}} \cr & \Rightarrow {\text{Share of B}} = 5x \cr & \Rightarrow {\text{Share of A}} = 2x \cr & \therefore {\text{Share of (B}} - {\text{A)}} = 3x \cr & \Rightarrow 3 \times 11.50 = {\text{Rs}}.34.50 \cr\end{align}

Length : Width

5x :: 2x

Width ⇒ 2x ⇒ 40m

x ⇒ 20m

∴ Length ⇒ 5 $\times$ 20 = 100m

\begin{align} & {\text{Let}}\, {\text{the}}\, {\text{fourth}}\, {\text{proportional}}\, {\text{to}}\, 5, \, 8, \, 15\, {\text{be}}\, x. \cr & {\text{Then}}, \, 5:8:15:x \cr & \Rightarrow 5x = \left( {8 \times 15} \right) \cr & x = \frac{{\left( {8 \times 15} \right)}}{5} = 24 \cr\end{align}