Answer:
Sunayana's income is ₹25000 and expenditures are ₹15000.
Step-by-step explanation:
Let i denote the monthly income and e denote the expenditures.
We know that the ratio of the monthly income to expenditure is 5:3. So, we can write the following proportion:
![\frac{i}{e}=\frac{5}{3}](https://tex.z-dn.net/?f=%5Cfrac%7Bi%7D%7Be%7D%3D%5Cfrac%7B5%7D%7B3%7D)
Let's multiply both sides by e. This yields:
![i=\frac{5}{3}e](https://tex.z-dn.net/?f=i%3D%5Cfrac%7B5%7D%7B3%7De)
We know that when the income is <em>increased</em> by 5000 and the expenditures are <em>decreased </em>by 3000, the new ratio is 5:2. So, we can write the following proportion:
![\frac{i+5000}{e-3000}=\frac{5}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bi%2B5000%7D%7Be-3000%7D%3D%5Cfrac%7B5%7D%7B2%7D)
Let's multiply both sides by
:
![i+5000=\frac{5}{2}(e-3000)](https://tex.z-dn.net/?f=i%2B5000%3D%5Cfrac%7B5%7D%7B2%7D%28e-3000%29)
Since we know that
, substitute:
![\frac{5}{3}e+5000=\frac{5}{2}(e-3000)](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B3%7De%2B5000%3D%5Cfrac%7B5%7D%7B2%7D%28e-3000%29)
So, let's solve for the expenditures. Distribute the right:
![\frac{5}{3}e+5000=\frac{5}{2}e-7500](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B3%7De%2B5000%3D%5Cfrac%7B5%7D%7B2%7De-7500)
Subtract
from both sides:
![-\frac{5}{6}e+5000=-7500](https://tex.z-dn.net/?f=-%5Cfrac%7B5%7D%7B6%7De%2B5000%3D-7500)
Subtract 5000 from both sides:
![-\frac{5}{6}e=-12500](https://tex.z-dn.net/?f=-%5Cfrac%7B5%7D%7B6%7De%3D-12500)
Multiply both sides by -6/5. So, the expenditures are:
![e=\text{Rs }15000](https://tex.z-dn.net/?f=e%3D%5Ctext%7BRs%20%7D15000)
We can use the original ratio to find Sunayana's income:
![i=\frac{5}{3}e](https://tex.z-dn.net/?f=i%3D%5Cfrac%7B5%7D%7B3%7De)
Substitute 15000 for e. Evaluate:
![i=\frac{5}{3}(15000)=\text{Rs }25000](https://tex.z-dn.net/?f=i%3D%5Cfrac%7B5%7D%7B3%7D%2815000%29%3D%5Ctext%7BRs%20%7D25000)
So, Sunayana's income is ₹25000 and expenditures are ₹15000.
And we're done!
Edit: Wrong currency, sorry about that!