Question

The incomes of A and B are in the ratio 3:5 and their expenditures are in the ratio 2:3 . If A save Rs.8000 and B saves Rs.15000, then the income of A is plz ans fastly will mark u as the brainliest

Answer 1

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✴ Required Answer:

✏ GiveN:

• Ratio of incomes of A and B = 3:5
• Ratio of their expenditures = 2:3
• A saves Rs. 8000
• And, B saves Rs. 15000

✏ To FinD:

• Find the income of A

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✴ How to solve?

Considering the incomes of A and B in terms of any variable and same for their expenditures. We know that expenditure + saving = incomes. In the question, saving is given and ratio of income and expenditures are given. Form here, we can frame equations and solve the question.

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✴ Solution:

Let the incomes of A be 3x and B be 5x

And, expenditures of A be 2y and B be 3y

Saving of A = Rs.8000 and Saving of B = Rs. 15000

We know, Expenditures + Savings = Incomes

So, let's write the equation for A and B,

According to statement,

❇ A

$\large{ \rm{ \longrightarrow \: 2y + 8000 = 3x}} \\ \\ \large{ \rm{ \longrightarrow \: 3x - 2y = 8000 - - - - (1)}}$

❇ B

$\large{ \rm{ \longrightarrow \: 3y + 15000 = 5x}} \\ \\ \large{ \rm{ \longrightarrow \: 5x - 3y = 15000 - - - - - (2)}}$

By using elimination method,

Multiplying eq.(1) with 3,

$\large{ \rm{ \longrightarrow \: 3(3x - 2y) = 24000}} \\ \\ \large{ \rm{ \longrightarrow \: 9x - 6y = 24000}}$

Multiplying eq.(2) with 2,

$\large{ \rm{ \longrightarrow \: 2(5x - 3y) = 30000}} \\ \\ \large{ \rm{ \longrightarrow \: 10x - 6y = 30000}}$

Subtracting eq.(1) from eq.(2)

$\large{ \rm{ \longrightarrow \: 10x - 6y - (9x - 6y) = 30000 - 24000}} \\ \\ \large{ \rm{ \longrightarrow \: 10x - \cancel{6y} - 9x + \cancel{ 6y }= 6000}} \\ \\ \large{ \rm{ \longrightarrow \: x = 6000}}$

So, Income of A,

$\large{ \rm{ \longrightarrow \: \boxed{ \red{ \rm{3x = 18000}}}}} \\ \\ \large{ \therefore{ \underline{ \underline{ \purple{ \rm{Hence \: solved \: \dag}}}}}}$

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