Math, asked by shubhamsorte94, 4 months ago


5) The ratio of income of Ravi and Pankaj is 9 : 5 and the ratio of their expenditures is 7 : 3. Each of them saves Rs. 1680 monthly. Find their monthly income.

Answers

Answered by ImperialGladiator
16

Answer :

  • Ravi = ₹7,560
  • Pankaj = ₹4,200

Explanation :

Income ratio of -

  • Ravi : Pankaj = 9 : 5

Saving ratio of -

  • Ravi : Pankaj = 7 : 3

But, each of them saves ₹1,680 monthly.

Let's assume the monthly income of -

  • Ravi = 9x
  • Pankaj = 5x

And also, monthly expenditure of -

  • Ravi = 7y
  • Pankaj = 3y

We know that,

  • Savings = income - expenditure

∴ Ravi's savings - {(9x - 7y) = 1,680 \:\:\:\: . . . . (i)}

∴ Pankaj's savings - {(5x - 3y) = 1,680 \:\:\:\: . . . . (ii)}

Elimination method :

Multiplying eq.(i) by 5 and also, eq.(ii) by 9

We get,

{45x - 35y = 8400 \:\:\:\: . . . . (i)}

{45x - 27y = 15,120 \:\:\:\: . . . . (ii)}

Solving eq.(i) & eq.(ii) :-

 45x - 35y = 8400 \\{ \underline{45x - 27y = 15120}} \\ \tiny( - )   \quad( + ) \qquad \:  \:  \:  \qquad (  -  )\qquad\\  \implies \:    - 8y =  - 6720 \\  \implies 8y = 6720 \\  \implies y =  \frac{6720}{8}  \\  \therefore \: y = 840

Substitute the value of \boldsymbol y in eq.(i) :-

 \implies \: 9x - 7y = 1680 \\

\implies \: 9(840) - 7y = 1680 \\

\implies \: 7560 - 7y = 1680 \\

\implies \: 7560 - 1680 = 7y \\

\implies \: 5880 = 7y \\

\implies \:  \dfrac{5880}{7}  = y  \\

\implies \: 840 = y \\

\therefore \boldsymbol{ x = y = 840}

Therefore, the monthly income of -

  • Ravi = 9x = 9(840) = ₹7,560
  • Pankaj = 5x = 5(840) = ₹4,200
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