the ratio of income of two persons is 11:3 & ratio of expentitures is 5:1 if each of them manages to save rupees 1000 per month find their monthly income and expenditures

Question

Linear equation in two veriables

Answer 1

Let first person's income be AI and the expenditure AE; the second person's income is BI and expenditure BE.

11/3=AI/BI and 5=AE/BE. Savings are AI-AE=BI-BE=1000; substitute for BI and BE:

AI-AE=3AI/11-AE/5=1000.

55AI-55AE=15AI-11AE=55000; so (55-15)AI=(55-11)AE, 40AI=44AE, 10AI=11AE. So 55AE=50AI.

55AI-50AI=55000, 5AI=55000 so AI=Rs11000. 11AE=10AI=110000, so AE=Rs10000.

BI=3AI/11=Rs33000/11=Rs3000; BE=AE/5=Rs10000/5=Rs2000.

First person's income and expenditure is Rs11000, Rs10000. (Savings Rs1000)

Second person's income and expenditure is Rs3000, Rs2000. (Savings Rs1000)