question_answer

The ratio of incomes of two persons is 5 : 3 and that of their expenditures is 9 : 5. Find the income of each person, if they save Rs.1300 and Rs. 900 respectively                                   

A)  Rs. 4000, Rs. 2400        

B)  Rs. 3000, Rs. 1800   

C)  Rs. 5000, Rs. 3000        

D)  Rs. 4500, Rs. 2700 

Correct Answer: A

Solution :

Let incomes of two persons be 5x and 3x and their expenses be 9y and 5y, respectively. Then,    \[5x-9y=1300\]                          ?(i)     and       \[3x-5y=900\]                            ?(ii) By fix Eqs (ii) \[-\,\,5\times \]Eqs (i), we get \[\Rightarrow \]   \[x=800\] Now, income of first person \[=5x=5\times 800\] = Rs. 4000 and that of second person\[=3x=3\times 800\]= Rs. 2400