Question

The monthly incomes of A and B are in the
ratio 7:5 and their excpenditures are in the
giatio 3:2If each
saves F 1500
роя. month
find their monthly incomes​

Answer 1

$\large\bf\underline \purple{Correct\:Question:-}$

The monthly incomes of A and B are in the ratio 7:5 and their expenditures ratio is 3:2 .If each saves Rs 1500. Then find their monthly income.

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$\large\bf\underline \green{Given:-}$

• Monthly incomes ratio of A and B = 7:5

• Ratio of expenditures of A and B = 3:2

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

• Monthly incomes of both A and B.

$\huge\bf\underline \red{Solution:-}$

• Let the monthly income of A = 7x
• Let the monthly income of B = 5x

Let their expenditures be 3y and 2y.

• Monthly savings of A = ₹(7x - 3y)
• Monthly savings of B = ₹(5x - 2y)

But monthly savings of both A and B is ₹ 1500

∴⠀$: \implies \rm\:7x - 3y = 1500 .............(i)$

$: \implies \rm\:5x - 2y = 1500 .............(ii)$

Multiplying (i) by 2 and (ii) by 3

$: \implies \rm\:$(7x - 3y = 1500) ×2

$: \implies \rm\:$(5x-2y = 1500)×3

we get,

$: \implies \rm\:14x-6y=3000.........(iii)$

$: \implies \rm\:15x-6y=4500.........(iv)$

On solving (iii) and (iv) equations by elimination method,

14x - 6y = 3000

15x - 6y = 4500

--⠀⠀⠀+⠀⠀⠀--⠀

-x ⠀⠀⠀⠀= -1500

x = 1500

So,

Monthly income of A = 7x

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$: \implies \rm\:7\times1500$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$: \implies \rm\pink{\:10500}$

Monthly income of B = 5x

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$: \implies \rm\:5\times1500$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$: \implies \rm\pink{\:7500}$

Answer 2

$\bold\blue{Correct \ Question:}$

$\sf{The \ monthly \ incomes \ of \ A \ and \ B}$

$\sf{in \ the \ ratio \ 7:5 \ and \ their \ expenditures}$

$\sf{are \ in \ ratio \ 3:2. \ If \ each \ saves}$

$\sf{Rs \ 1500 \ per \ month. \ Find \ their}$

$\sf{monthly \ incomes.}$

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{Incomes \ of \ A \ and \ B \ are}$

$\sf{Rs \ 10500 \ and \ Rs \ 7500 \ respectively.}$

$\sf\orange{\underline{\underline{Given:}}}$

$\sf{For \ A \ and \ B,}$

$\sf{\implies{Ratio \ of \ monthly \ income=7:5}}$

$\sf{\implies{Ratio \ of \ saving \ per \ month=3:2}}$

$\sf{\implies{Each \ saves \ Rs \ 1500 \ per \ month}}$

$\sf\pink{\underline{\underline{To \ find:}}}$

$\sf{Their \ monthly \ incomes.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Let \ common \ multiple \ for \ monthly}$

$\sf{income \ be \ x.}$

$\sf{\implies{\therefore{Monthly \ income \ of \ A=7x}}}$

$\sf{\implies{Monthly \ income \ of \ B=5x}}$

$\sf{Let \ the \ common \ multiple \ of }$

$\sf{expenditures \ be \ y.}$

$\sf{\implies{Expenditure \ of \ A=3y}}$

$\sf{\implies{Expenditure \ of \ B=2y}}$

$\boxed{\sf{Saving=Income \ - \ Expenditure}}$

$\sf{But, \ each \ saves \ Rs \ 1500 \ per \ month.}$

$\sf{\therefore{7x-3y=1500...(1)}}$

$\sf{5x-2y=1500...(2)}$

$\sf{Multiply \ equation \ (1) \ by \ 2, \ we \ get}$

$\sf{14x-6y=3000...(3)}$

$\sf{Multiply \ equation \ (2) \ by \ 3, \ we \ get}$

$\sf{15x-6y=4500...(4)}$

$\sf{Subtract \ equation \ (3) \ from \ equation \ (4)}$

$\sf{15x-6y=4500}$

$\sf{-}$

$\sf{14x-6y=3000}$

____________________

$\sf{\implies{x=1500}}$

$\sf{\therefore{Income \ of \ A=7(1500)}}$

$\sf{\implies{Income \ of \ A=Rs \ 10500}}$

$\sf{Income \ of \ B=5(1500)}$

$\sf{\implies{Income \ of \ B=Rs \ 7500}}$

$\sf\purple{\tt{\therefore{Incomes \ of \ A \ and \ B \ are}}}$

$\sf\purple{\tt{Rs \ 10500 \ and \ Rs \ 7500 \ respectively.}}$