Question

i. One says,” Give me a hundred, friend ! I shall then become twice as rich as

you”.The other replies,” If you give me ten , I shall be six times as rich as you”.

Tell me what is the amount of their capital?​

Answer 1

$\LARGE\textsf{\textcolor{red}{SOLUTION :-}}$

➠ $\large\textsf{Let the initial capital} \\ \large\textsf{of first person be ' x '}$

➠ $\large\textsf{Let the initial capital}\\ \large\textsf{of second person be' y '}$

$\large\textsf{\textcolor{red}{According to the 1st condition :-}}$

$\large\therefore\textsf{x + 100 = 2( y - 100 )}$

$\large\therefore\textsf{x + 100 = 2y - 200}$

$\large\therefore\textsf{x - 2y = -200 - 100}$

$\large\therefore\textsf{x - 2y = - 300...... ( i )}$

$\large\textsf{\textcolor{red}{According to the 2nd condition :-}}$

$\large\therefore\textsf{y + 10 = 6 ( x - 10 )}$

$\large\therefore\textsf{y + 10 = 6x - 60}$

$\large\therefore\textsf{- 6x + y = - 60 - 10}$

$\large\therefore\textsf{- 6x + y = -70..... ( ii )}$

$\large\textsf{\textcolor{red}{Multiple equation ( ii ) by 2 :-}}$

$\large\therefore\textsf{2 ( - 6x + y ) = - 70 × 2}$

$\large\therefore\textsf{-12x + 2y = -140....... ( iii )}$

$\large\textsf{\textcolor{red}{Add eq. ( i ) and ( iii ) :-}}$

$\large\textsf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:x - 2y = - 300}\\ \large\textsf{( + ) \: \: \: \: - 12x + 2y = - 140} \\ \large\textsf{---------------------------------------} \\ \large\textsf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - 11x = - 440} \\ \\ \large\textsf{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = }{\cancel\frac{ - 440}{ - 11}} \\ \\ \large\textsf{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = 40}$

$\large\textsf{\textcolor{red}{Substituting the value of ' x ' in ( i ) :-}}$

$\large\therefore\textsf{40 - 2y = - 300}$

$\large\therefore\textsf{- 2y = - 300 - 40}$

$\large\therefore\textsf{- 2y = - 340}$

$\large\therefore\textsf{y =} \cancel\frac{-340}{-2}$

$\large\therefore\textsf{y = 170}$

$\large\textsf{\textcolor{red}{So,}}$

$\large\therefore\boxed{\textsf{\textcolor{orange}{1st person have 40 Rs.}}}$

$\large\therefore\boxed{\textsf{\textcolor{orange}{2nd person have 170 Rs.}}}$