mahesh spends 20% of his income on house rent, 30% of the remaining on food ,40% of the remaining on education , 50% of the remaining on other expanses and save the remaining amount every month .what percent of the total income does he save every month?

Let's analyze the problem step-by-step.

Problem Restatement

Mahesh spends his income in the following way:

• He spends 25\frac{2}{5}52​ of his income on house rent.
• Then he spends 35\frac{3}{5}53​ of the remaining on food.
• Then he spends 45\frac{4}{5}54​ of the new remaining on education.
• Then he spends 15\frac{1}{5}51​ of the new remaining on other expenses.
• The rest is saved.

We need to find what percent of the total income he saves every month.

Step-by-step Solution

Let's assume Mahesh's total income is III.

Step 1: House rent

He spends 25\frac{2}{5}52​ of III on house rent. Remaining income after house rent:

I−25I=35II-\frac{2}{5}I=\frac{3}{5}II−52​I=53​I

Step 2: Food

He spends 35\frac{3}{5}53​ of the remaining 35I\frac{3}{5}I53​I on food. Amount spent on food:

35×35I=925I\frac{3}{5}\times \frac{3}{5}I=\frac{9}{25}I53​×53​I=259​I

Remaining income after food:

35I−925I=1525I−925I=625I\frac{3}{5}I-\frac{9}{25}I=\frac{15}{25}I-\frac{9}{25}I=\frac{6}{25}I53​I−259​I=2515​I−259​I=256​I

Step 3: Education

He spends 45\frac{4}{5}54​ of the remaining 625I\frac{6}{25}I256​I on education. Amount spent on education:

45×625I=24125I\frac{4}{5}\times \frac{6}{25}I=\frac{24}{125}I54​×256​I=12524​I

Remaining income after education:

625I−24125I=30125I−24125I=6125I\frac{6}{25}I-\frac{24}{125}I=\frac{30}{125}I-\frac{24}{125}I=\frac{6}{125}I256​I−12524​I=12530​I−12524​I=1256​I

Step 4: Other expenses

He spends 15\frac{1}{5}51​ of the remaining 6125I\frac{6}{125}I1256​I on other expenses. Amount spent on other expenses:

15×6125I=6625I\frac{1}{5}\times \frac{6}{125}I=\frac{6}{625}I51​×1256​I=6256​I

Remaining income after other expenses:

6125I−6625I=30625I−6625I=24625I\frac{6}{125}I-\frac{6}{625}I=\frac{30}{625}I-\frac{6}{625}I=\frac{24}{625}I1256​I−6256​I=62530​I−6256​I=62524​I

Step 5: Savings

The remaining amount is saved:

Savings=24625I\text{Savings}=\frac{24}{625}ISavings=62524​I

Final answer: Percentage saved

Percentage saved=SavingsI×100=24625×100=2400625=3.84%\text{Percentage saved}=\frac{\text{Savings}}{I}\times 100=\frac{24}{625}\times 100=\frac{2400}{625}=3.84%Percentage saved=ISavings​×100=62524​×100=6252400​=3.84%

Mahesh saves 3.84% of his total income every month.