Math, asked by vaishnavdrd70, 10 months ago

the ratio of the incomes of Amit and Rajiv is 3 : 5 and the ratio of their expenditures is 5:9 if each person saved rupees 5000 then their income of Rajiv is

Answers

Answered by Anonymous
24

 \large\bf\underline{Given:-}

  • Ratio of income of Amit and Rajiv is 3:5
  • Ratio of their expenditures is 5:9
  • each of them saves 5000

 \large\bf\underline {To \: find:-}

  • Income of Rajiv

 \huge\bf\underline{Solution:-}

Let the income of Amit and Rajeev be 3x and 5x

Let their expenditures be 5y and 9y.

We know that ,

(income - expenditures) = savings.

Savings of Amit

 \leadsto \rm \:  3x - 5y = 5000 \: ....(i)

Savings of Rajiv

 \leadsto \rm \: 5x - 9y = 5000.........(ii)

Multiply eq. (i) by 5 and eq. (ii) by 3

we get,

 \rm \: (3x - 5y = 5000) \times 5 \\ \rm \:( 5x - 9y = 5000) \times 3 \\  \:  \\ \rm \:15x - 25y = 25000........(iii) \\\rm \: 15x - 27y = 15000..........(iv)

Solving eq. (iii) and (iv)

\rm \:15x - 25y = 25000 \\ \rm \:15x - 27y = 15000 \\  \:  \:  -  \:  \:  \:  \:  \:  \:  \:  \:  + \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   -  \\  \underline{ \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: } \\ \rm \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: 2y = 10000 \\  \rm \:\: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: y =   \cancel\dfrac{10000}{2}  \\  \\ \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \bf \: y = 5000

putting value of y in eq. (iv)

 \longmapsto \rm \: 15x - 27y = 15000 \\   \longmapsto \rm \:15x - 27(5000) = 15000 \\   \longmapsto \rm \:15x - 135000 = 15000 \\   \longmapsto \rm \:15x = 15000 + 135000 \\ \longmapsto \rm \:15x = 150000 \\ \longmapsto \rm \:x =   \cancel\dfrac{150000}{15}  \\  \longmapsto \bf \:x = 10000

So, Rajiv's income = 5x = 10000×5

Rajiv's income = Rs 50000

Another method :-

we know that,

Savings = (income - expenditures)

Then,

Income = savings + expenditures.

expenditures of Rajiv = 9y = 9×5000

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 45000

Rajiv's income = 5000 + 45000

Rajiv's income = 50000

Answered by Anonymous
40

Answer:

⋆ DIAGRAM :

\boxed{\setlength{\unitlength}{.8mm}\begin{picture}(40,22)\thicklines\put(25,15){\vector(1,-1){10}}\put(15,15){\vector(-1,-1){10}}\put(9,18){\sf\large\star$\:\underline{Income}}\put(0,1){\sf{Expense}}\put(18,1){+}\put(25,1){\sf{Saving}}\end{picture}}\quad\boxed{\begin{minipage}{5.2 cm}\qquad\qquad\quad\bf{Amit -}\qquad\:\bf{Rajiv -}\\\\\sf Income\quad\:\!= 3\qquad\quad:\quad\qquad5\\Expenses = 5\qquad\quad:\quad\qquad9\\Savings\quad=\:Rs.\:5000\qquad Rs.\:5000\end{minipage}}

⠀⠀⠀\rule{160}{0.8}

Let the Income of Amit and Rajiv be 3x and 5x respectively.

\underline{\boldsymbol{According\: to \:the\: Question\:now :}}

:\implies\sf \dfrac{Amit_{(Income)}-Saving}{Rajiv_{(Income)}-Saving}=\dfrac{Amit_{(Expenditure)}}{Rajiv_{(Expenditure)}}\\\\\\:\implies\sf \dfrac{3x - 5000}{5x - 5000} = \dfrac{5}{9}\\\\\\:\implies\sf (3x - 5000) \times 9 = 5 \times (5x - 5000)\\\\\\:\implies\sf 27x - 45000 = 25x - 25000\\\\\\:\implies\sf 27x - 25x = 45000 - 25000\\\\\\:\implies\sf 2x = 20000\\\\\\:\implies\sf x = \dfrac{20000}{2}\\\\\\:\implies\sf x = Rs.\:10000

\rule{150}{1.5}

\underline{\boldsymbol{Income\: of \:Rajiv :}}

\dashrightarrow\sf\:\:Rajiv_{(Income)}=5x\\\\\\\dashrightarrow\sf\:\:Rajiv_{(Income)}=5 \times Rs.\:10000\\\\\\\dashrightarrow\:\:\underline{\boxed{\sf Rajiv_{(Income)}=Rs.\:50000}}

\therefore\:\underline{\textsf{Hence, Income of Rajiv is \textbf{Rs. 50,000}}}.

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