# 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?

## 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**.