d)) The ratio of the monthly income and expenditure of Sunayana is 5 : 3. If she
increases her income by Rs 5,000 and decreases the expenditure by Rs 3,000, the
new ratio becomes 5:2. Find her income and expenditure.

We know that when the income is increased by 5000 and the expenditures are decreased by 3000, the new ratio is 5:2. So, we can write the following proportion:

[tex]\displaystyle \frac{i+5000}{e-3000}=\frac{5}{2}[/tex]

Let's multiply both sides by [tex](e-3000)[/tex]:

[tex]\displaystyle i+5000=\frac{5}{2}(e-3000)[/tex]

Since we know that [tex]i=\frac{5}{3}e[/tex], substitute:

[tex]\displaystyle \frac{5}{3}e+5000=\frac{5}{2}(e-3000)[/tex]

So, let's solve for the expenditures. Distribute the right:

[tex]\displaystyle \frac{5}{3}e+5000=\frac{5}{2}e-7500[/tex]

Subtract [tex]\frac{5}{2}e[/tex] from both sides:

[tex]\displaystyle -\frac{5}{6}e+5000=-7500[/tex]

Subtract 5000 from both sides:

[tex]\displaystyle -\frac{5}{6}e=-12500[/tex]

Multiply both sides by -6/5. So, the expenditures are:

[tex]e=\text{Rs }15000[/tex]

We can use the original ratio to find Sunayana's income:

[tex]\displaystyle i=\frac{5}{3}e[/tex]

Substitute 15000 for e. Evaluate:

[tex]\displaystyle i=\frac{5}{3}(15000)=\text{Rs }25000[/tex]

So, Sunayana's income is ₹25000 and expenditures are ₹15000.

And we're done!

tramserran tramserran · Answer 2 · 2020-10-10T11:41:21+02:00

Answer: Income = 25000, Expenditures = 15000

Step-by-step explanation:

A ratio of 5:3 can also be written in fraction form as [tex]\dfrac{5}{3}[/tex] (which is in simplified format from [tex]\dfrac{5x}{3x}[/tex]).

Adding 5000 to 5x results in 5x + 5000

Subtracting 3000 from 3x results in 3x - 3000

--> [tex]\dfrac{5x+5000}{3x-3000}[/tex]

The new ratio of 5:2 can be written in simplified fraction form of [tex]\dfrac{5}{2}[/tex].

Set the fractions equal to each. Then cross multiply and solve for x.

[tex]\dfrac{5x+5000}{3x-3000}=\dfrac{5}{2}[/tex]

5(3x - 3000) = 2(5x + 5000) Cross multiplied

15x - 15000 = 10x + 10000 Distributed

5x - 15000 = 10000 Subtracted 0x from both sides

5x = 25000 Added 15000 to both sides

x = 5000 Divided 5 from both sides

The original ratio of 5 : 3 --> 5x:3x

where 5x is the income and 3x is the expenditures results in:

income = 5x expenditures = 3x

= 5(5000) = 3(5000)

= 25000 = 15000

d)) The ratio of the monthly income and expenditure of Sunayana is 5 : 3. If sheincreases her income by Rs 5,000 and decreases the expenditure by Rs 3,000, thenew ratio becomes 5:2. Find her income and expenditure.​

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Otras preguntas

d)) The ratio of the monthly income and expenditure of Sunayana is 5 : 3. If she
increases her income by Rs 5,000 and decreases the expenditure by Rs 3,000, the
new ratio becomes 5:2. Find her income and expenditure.