Question

A and B have some money with them. A said to B,'if you give me Rs 100, my money will become 75% of the money left with you'. "B said to A" instead if you give me Rs 100, your money will become 40% of my money. How much money did A and B have originally?
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Answer 1

Dear student,

$$\begin{gathered} \mathrm{Let}\mathrm{Rs}.\mathrm{a}\mathrm{be}\mathrm{the}\mathrm{money}\mathrm{with}\mathrm{A}\mathrm{and}\mathrm{Rs}.\mathrm{b}\mathrm{be}\mathrm{the}\mathrm{money}\mathrm{with}\mathrm{B}. \\ \mathrm{Then},\mathrm{according}\mathrm{to}\mathrm{the}\mathrm{question}: \\ (\mathrm{a}+100)\hspace{0.17em}=0.75(\mathrm{b}-100)\hspace{0.17em}----\left(1\right) \\ 0.4(\mathrm{b}+100)=(\mathrm{a}-100)----\left(2\right) \\ \mathrm{Simplifying}\mathrm{equations}\left(1\right)\mathrm{and}\left(2\right),\mathrm{We}\mathrm{get}: \\ \mathrm{a}-0.75\mathrm{b}=-175---\left(3\right) \\ -\mathrm{a}+\hspace{0.17em}0.4\mathrm{b}=-140---\left(4\right) \\ \mathrm{Adding}\left(3\right)\mathrm{and}\left(4\right),\mathrm{we}\mathrm{get} \\ -0.35\mathrm{b}=-315\Rightarrow \mathrm{b}=900 \\ \mathrm{Now},\mathrm{from}\left(3\right),\mathrm{we}\mathrm{get}\mathrm{a}=500 \\ \mathrm{Thus},\mathrm{A}\mathrm{and}\mathrm{B}\mathrm{originally}\mathrm{had}\mathrm{Rs}.500\mathrm{and}\mathrm{Rs}.900\mathrm{respectively}. \end{gathered}$$

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