Question

the ratio of incomes of 2 persons is 9:7 and the ratio of their expenses is 4:3 ,if each of them manages to save its 2000 per month ,find their monthly incomes
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Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$  

Assumption

Incomes of the two person be

9p and 7p

Also,

${\boxed{\sf\:{Expenditures\:=\:4n\;and\;3n}}}}$

Hence now,

${\boxed{\sf\:{Create\;an\;Equation}}}}$

9p - 4n = 2000 .............. (1)

7p - 3n = 2000 .............. (2)

By Method here multiply (1) by 3 and (2) by 4 we get,

27p - 12n = 6000 ............... (3)

28p - 12n = 8000 ............... (4)

Here,

Co- Efficient of n is same hence, subtract (3) from (4)

(28p - 27p) - (12n - 12n) = 8000 - 6000

p = 2000

${\boxed{\sf\:{Putting\:value\;of\;p\;in\;(1)}}}}$

⇒ 9(2000) - 4n = 2000

⇒ 18000 - 4n = 2000

⇒ 18000 - 2000 = 4n

⇒ 16000 = 4n

${\implies\dfrac{16000}{4}=n}$        

⇒ n = 4000

Therefore,

p = 2000, n = 4000.

Hence,

First Person Income  

= 9p

= 9 × 2000

= 18000

Second Person Income

= 7p

= 7 × 2000

= 14000

Monthly incomes of the persons

$\Large{\boxed{\bigstar{\sf\:{Rs.18,000\;and\;14,000}}}}$

Answer 2

Answer:

$\bf\purple{Monthly\:income\:of\:1st\:person=Rs18000}$

$\bf\purple{Monthly\:income\:of\:2nd\:person=Rs.14000}$

_____________________

Given that,

• Ratio of income of 2 persons=9:7
• Ratio of expenses = 4 : 3
• Each of them manages to save=2000
• Their monthly income = ?

Let the income of 1st person be 9x

And the income of 2nd person be 7x

_______________________

Let the expenses of 1st person be 4y

And the expenses of 2nd person be 3y

According to question:-

$\tt 9x - 4y = 2000 \: \: \: \: (eq.1)$

$\tt 7x - 3y = 2000 \: \: \: \: (eq.2)$

Now multiplying (eq.1) by 3 and (eq.2) by 4 ,and substracting we get,

$\Rightarrow\tt (27x-12y)-(28x - 12y) = 6000 - 8000$

$\Rightarrow\tt - x = -2000$

$\Rightarrow\tt x = 2000$

________________________

Now putting values we get,

$\leadsto\tt Income\:of\:1st\:person= 9x = 9\times 2000 \\ \\ \leadsto\tt Income = Rs.18000$

________________________

$\leadsto\tt Income\:of\:2nd\:person=7x = 7 \times 2000 \\ \\ \leadsto\tt Income = Rs.14000$

$\therefore\tt {\underline{Income \:of\:1st\:person = Rs.18000 }}$

$\therefore\tt {\underline{Income\:of \:2nd\:person=Rs.14000}}$