A spend 10% of his monthly income on rent, 20% of the remaining on food and 50% of the remaining on travelling. If the difference between the amount he spends on travelling and that on rent is Rs.13000, then find the monthly income (in Rs.) of A?

Correct Option: Rs.50000

Step-by-Step Explanation:

Step 1: Define the variables and total income.
Let the total monthly income of A be $x$ rupees.

Step 2: Calculate the expenditure on rent.
A spends 10% of his monthly income on rent.
Amount spent on rent = 10% of $x$

$\text{Rent}=\frac{10}{100}\times x=0.10x$

Step 3: Calculate the remaining income after rent.
Remaining amount after paying rent:

${\text{Remaining}}_1=x-0.10x=0.90x$

Step 4: Calculate the expenditure on food.
A spends 20% of the remaining income on food.
Amount spent on food = 20% of $0.90x$

$\text{Food}=\frac{20}{100}\times 0.90x=0.18x$

Step 5: Calculate the remaining income after food.
Remaining amount after spending on food:

${\text{Remaining}}_2=0.90x-0.18x=0.72x$

Step 6: Calculate the expenditure on travelling.
A spends 50% of the remaining income on travelling.
Amount spent on travelling = 50% of $0.72x$

$\text{Travelling}=\frac{50}{100}\times 0.72x=0.36x$

Step 7: Formulate the equation using the given difference.
The difference between the amount spent on travelling and rent is given as Rs. 13,000.
Travelling - Rent = 13,000

$0.36x-0.10x=13000$

$0.26x=13000$

Step 8: Solve for the monthly income ($x$).

$x=\frac{13000}{0.26}$

$x=\frac{1300000}{26}=50000$

Thus, the monthly income of A is Rs.50000.