Question

38. The ratio of incomes of two persons is 9.7 and the ratio of their expenditures is 43. It each of the manage to save 2,000 per month, find their monthly incomes.​

Answer 1

Question : The ratio of incomes of two persons is 9:7 and the ratio of their expenditures is 4:3. It each of the manage to save Rs 2,000 per month, find their monthly incomes.

Solution : Now, according to given,

The ratio of incomes of two persons is 9:7

• Let, income of first person be 9x and income of second person be 7x.

Similarly,

The ratio of expenditures of two persons is 4:3.

• Let, expenditure of first person be 4y and expenditure of second person be 3y.

Here, we know that,

⟹ income - expenditure = savings

Hence, for first person

⟹ 9x - 4y = 2000 ----{ 1 }

Similarly, for second person

⟹ 7x - 3y = 2000 ----{ 2 }

Now, multiply eq. { 1 } by 3, we get

⟹ 27x - 12y = 6000 ----{ 3 }

Similarly, multiply eq. { 2 } by 4, we get

⟹ 28x - 12y = 8000 ----{ 4 }

Now, subtract eq. { 4 } from eq. { 3 }

27x - 12y = 6000

- ( 28x - 12y = 8000 )

_______________________

- x = - 2000

x = 2000

Here, we know that, income of first person is 9x, hence,

• 9x = 9 * 2000 = Rs 18000

Similarly we know income of second person is 7x.

• 7x = 7 * 2000 = Rs 14000

Answer : Hence monthly income of first person is Rs 18000 and monthly income of second person is Rs 14000.

{More info : To find expenditure ?

Put value of x in eq. { 1 }

⟹ 9x - 4y = 2000

⟹ 9(2000) - 4y = 2000

⟹ 18000 - 4y = 2000

⟹ - 4y = 2000 - 18000

⟹ - 4y = - 16000

⟹ 4y = 16000

⟹ y = 16000/4

⟹ y = 4000

Here we know, expenditure of first person is 4y and expenditure of second person is 3y. Hence,

• 4y = 4 * 4000 = Rs 16000
• 3y = 3 * 4000 = Rs 12000

Hence expenditure of first person is Rs 16000 and expenditure of second person is Rs 12000.}

Answer 2

Answer:

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