Ramu used to spend 72% of his income. His income has increased by 12%, and he increases his expenditure by 5%. If Ramu earlier saved y and after the increases he now saves x, then what is the value of ($\frac{x-y}{y}\times 100$)%?

Correct Answer: 30%

Let's solve the problem step-by-step to find the percentage increase in Ramu's savings.

Step 1: Understand the initial scenario (Before the increase)

Let Ramu's initial income be 100 units.

Given that Ramu initially spends 72% of his income:

Initial Expenditure = 72% of 100 = 72 units

Since Income = Expenditure + Savings, the initial savings ($y$) is calculated as:

$y=100-72=28$

So, initial savings $y=28$ units.

Step 2: Understand the new scenario (After the increases)

Ramu's income increases by 12%:

New Income = $100+(12\% \text{of} 100)=100+12=112$ units

Ramu increases his expenditure by 5%:

New Expenditure = $72+(5\% \text{of} 72)$

$5\% \text{of} 72=\frac{5}{100}\times 72=3.6$

New Expenditure = $72+3.6=75.6$ units

Ramu's new savings ($x$) is:

$x=\text{New Income}-\text{New Expenditure}$

$x=112-75.6=36.4$ units

Step 3: Calculate the required percentage value

We need to calculate the value of ($\frac{x-y}{y}\times 100$)%.

First, find the change in savings ($x-y$):

$x-y=36.4-28=8.4$

Now, calculate the percentage increase:

$\frac{x-y}{y}\times 100=\frac{8.4}{28}\times 100$

$\frac{8.4}{28}\times 100=0.3\times 100=30\%$

Thus, the value of ($\frac{x-y}{y}\times 100$)% is 30%.