The ratio of monthly income of x and y is 3 : 5 and the ratio of their expenditures is 1: 2. If each saves Rs. 5000 per month, then what will be the monthly income of x?
(A) 25000 (B) 20000 (С) 18000 (D) 15000
Let’s denote the monthly income of x as 3a and the monthly income of y as 5a, where ‘a’ is a common factor.
Similarly, let’s denote the monthly expenditures of x as 1b and the monthly expenditures of y as 2b, where ‘b’ is a common factor.
Given that each saves Rs. 5000 per month, we can set up the following equations:
Monthly savings of x = Monthly income of x – Monthly expenditures of x
Monthly savings of y = Monthly income of y – Monthly expenditures of y
So, we have:
\[3a – 1b = 5000\]
\[5a – 2b = 5000\]
Now, we need to solve these equations to find the values of ‘a’ and ‘b’. Once we have those, we can determine the monthly income of x (3a).
Let’s solve the system of equations:
\[3a – b = 5000\]
I made an error in setting up the equations. Let me correct that.
The correct equations are:
\[3a – 1b = 5000\]
\[5a – 2b = 5000\]
Now, let’s solve these equations:
Multiply the first equation by 2 to make the coefficients of ‘b’ the same:
\[6a – 2b = 10000\]
\[5a – 2b = 5000\]
Now, subtract the second equation from the first:
\[(6a – 2b) – (5a – 2b) = 10000 – 5000\]
\[a = 5000\]
Now that we have the value of ‘a’, we can find the monthly income of x (3a):
\[Monthly \ income \ of \ x = 3a = 3(5000) = 15000\]
So, the correct answer is (D) 15000.
