Question

The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. if each of them manages to save ₹ 2000 per month, then find their monthly incomes. Form a pair of linear equations from the above data and solve them by elimination method.
Also, verify the solution.​

Answer 1

Answer:

Question:-

The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. if each of them manages to save ₹ 2000 per month, then find their monthly incomes.

Solution:-

Answer:-

The ratio of incomes of two persons = 9:7

Let the income of first person = 9x,

the income of second person = 7x

The ratio of expenditure = 4:3

the expenditure of first person = 4y

the expenditure of second person = 3y

Saving of first person = income - expenditure

9x-4y = 2000------(1)

Saving of second person is

7x-3y = 2000--(2)

Solving (1) and (2), we get

x= 2000;

y= 4000

Therefore,

Monthly income of the firing person

= 9x = 9 × 2000 = Rs 18000b

Monthly income of the second person

= 7x = 7 × 2000 = Rs 14000

Step-by-step explanation:

$Hope \: it \: helps.$

Answer 2

$\huge\pink{\mid{\fbox{\tt{Answer}}\mid}}$

⇒ ₹18000 and ₹14000

$\huge\purple{\mid{\fbox{\tt{Solution}}\mid}}$

$\tt \red {GIVEN :}$

Ratio of incomes = 9 : 7

and ratio of their expenditures = 4 : 3

Saving of each persons = ₹2000

$\tt \orange{TO \: FIND :}$

the monthly incomes of each person

$\tt \green{CALCULATIONS : }$

Let incomes of two persons be 9x and 7x and their expenditures be 4y and 3y.

Then, linear equations so formed are :-

$\bf \red { 9x - 4y = 2000} \: \: \: \: \: \: \: ..eq(1)$

$\bf \pink {7x - 3y = 2000} \: \: \: \: \: \: \: ..eq(2)$

We make the coefficients of x numerically equal in both equations. On multiplying Eq.(i) by 7 and Eq.(ii) by 9, we get :-

$\bf \purple {\: 63x - 28y = 14000} \: \: \: \: \: ..eq(3)$

$\bf \green {\: 63x - 27y = 18000} \: \: \: \: \: ..eq(4)$

On subtracting Eq.(iv) from Eq.(iii), we get :-

$\tt \cancel{63x} - 28y = 14000$

$\tt \cancel{63x} - 27y = 18000$

-⠀⠀ +⠀⠀⠀

___________________________

$\tt0 \: \: \: \: \: - y = - 4000$

$\tt \cancel- y = \cancel- 4000$

$\tt \: y = 4000$

On putting y = 4000 in Eq.(i), we get :-

$\sf\implies9x - 4 × 4000 = 2000$

$\sf \implies9x - 16000 = 2000$

$\sf \implies9x = 16000 + 2000$

$\sf \implies 9x = 18000$

$\tt \implies \: x = 2000$

Thus, monthly income of both persons are 9(2000) and 7(2000), i.e. ₹18000 and ₹14000, respectively .

$\tt \blue{VERIFICATION }$

On putting x = 2000 and y = 4000 in Eqs. (i) and (ii) respectively, we get :-

From Eq.(i), LHS = 9x - 4y

$\sf \: = 9(2000) - 4(4000)$

$\sf \: = 18000 - 16000$

$\sf \: = 2000 = RHS$

From Eq.(ii), LHS = 7x - 3y

$\sf \: = 7(2000) - 3(4000)$

$\sf \: = 14000 - 12000$

$\sf \: = 2000 = RHS$

Hence, the solution is verified.