A started a business by investing some money and B invested Rs. 5000 each more than that of A. A remained in business for 5 months and B remained in business 1 month more than A. Out of total profit of Rs. 26000, B got Rs. 6000 more than A. Find capitals invested A and B ?

Let amount invested by A = Rs. x

	A	:	B
Capital →	x	:	(x + 5000)

$$\eqalign{ & {\text{According to the question,}} \cr & {\text{Share of A in profit}} \cr & = \frac{{\left( {26000 - 6000} \right)}}{2} \cr & = {\text{Rs}}{\text{. 10000}} \cr & {\text{Share of B in profit}} \cr & = \left( {26000 - 10000} \right) \cr & = {\text{Rs}}{\text{. 16000}} \cr & {\text{By using formulas:}} \cr & \boxed{\frac{{{{\text{C}}_{\text{1}}} \times {{\text{T}}_1}}}{{{{\text{C}}_{\text{2}}} \times {{\text{T}}_{\text{2}}}}} = \frac{{{{\text{P}}_{\text{1}}}}}{{{{\text{P}}_2}}}} \cr & \Leftrightarrow \frac{{x \times 5}}{{\left( {x + 5000} \right) \times 6}} = \frac{{10000}}{{16000}} \cr & \Leftrightarrow 4x = 3x + 15000 \cr & \Leftrightarrow x = {\text{Rs}}.15000 \cr & {\text{Required capital of A}} \cr & = {\text{Rs}}{\text{. 15000}} \cr & {\text{Required capital of B}} \cr & = \left( {15000 + 5000} \right) \cr & = {\text{Rs}}{\text{. 20000}} \cr} $$