Question

the ratio of incomes of two persons is 9:7 and the ratio of their expenditures is 4:3 if each if them saves rupees 2000 per month, find their monthly incomes​

Answer 1

Step-by-step explanation:

let their incomes be 9x and 7x respectively.

Savings of each= 2000

therefore there expenditures will be 9x-2000 and 7x-2000 respectively.

Now , expenditure ratio=4:3

therefore

4:3=9x-2000:7x-2000

4/3=9x-2000/7x-2000

4(7x-2000)=3(9x-2000) [ By transposing]

28x-8000=27x-6000

28x-27x=8000-6000

x=2000

therefore monthly income of first person=9x=9(2000)=18000

monthly income of second person=7x=7(2000)=14000

HOPE IT HELPS YOU BRO!!

Answer 2

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●Solution:

$\leadsto$Let us denote the incomes of the two person by rupees 9x and rupees 7x and their expenditures by rupees 4y and rupees 3y respectively. Then the equations formed in the situation is given by:

$\leadsto$9x - 4y =2000--》(1)

$\leadsto$7x - 3y = 2000--》(2)

$\leadsto<strong><u>$Step 1: Multiply Equation (1) by 3 and Equation (2) by 4 to make the coefficients of y equal. Then we get the equations:

and

$\leadsto$27x - 12y = 6000--》(3)

$\leadsto$28x - 12y = 8000--》(4)

$\leadsto$ Step 2: Subtract Equation (3) from Equation (4) to eliminate y, because the coefficients of y are the same. So, we get

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

$\leadsto$x =2000

$\leadsto$ Step 3: Substituting this value of x in (1), we get

$\leadsto$9(2000) - 4y = 2000

$\leadsto$y = 4000

$\leadsto$So, the solution of the equations is x=2000, y 4000. Therefore, the monthly incomes of the persons are rupees 18,000 and rupees 14,000, respectively,

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●Verification:

$\leadsto$ 18000 : 14000 = 9:7.

$\leadsto$Also, the ratio of their expenditures =

18000 - 2000: 14000 - 2000 = 16000 : 12000 = 4:3

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