If the salaries of two friends A and B are in the ratio of 3:4 and expenditure of A & B is in the ratio 1:2 and savings of the A and B is Rs 6000 each. If B again spends 20% of his salary, then find the new savings (in Rs) of B?

Correct Answer: 3600

Let's solve this step-by-step to find the new savings of B.

Step 1: Understand the given ratios and savings.
Let the salary of A be $3x$ and the salary of B be $4x$.
Let the expenditure of A be $1y$ and the expenditure of B be $2y$.

We know that: Savings = Salary - Expenditure
Both A and B save Rs 6000 each.

Step 2: Form equations using savings.
For A:

$3x-y=6000$

$4x-2y=6000$

Step 3: Solve for $x$ (and find B's initial salary).
From A's equation, we can write $y=3x-6000$.
Substitute this into B's equation:

$4x-2(3x-6000)=6000$

$4x-6x+12000=6000$

$-2x=6000-12000$

$-2x=-6000$

$x=3000$

Therefore, B's initial salary is:

$\text{Salary of B}=4x=4\times 3000=\text{Rs}12000$

Step 4: Find B's initial expenditure and savings.
If B's salary is Rs 12000 and initial savings are Rs 6000, then:

$\text{Initial Expenditure of B}=12000-6000=\text{Rs}6000$

Step 5: Calculate B's new expenditure and new savings.
B spends an additional 20% of his salary.

$\text{Additional expenditure}=20\%\text{of}12000=\frac{20}{100}\times 12000=\text{Rs}2400$

So, B's total new expenditure is:

$\text{Total Expenditure}=6000+2400=\text{Rs}8400$

Thus, B's new savings are:

$\text{New Savings}=\text{Salary}-\text{Total Expenditure}=12000-8400=\text{Rs}3600$

Hence, the new savings of B is 3600.