A person spends 10\% of his monthly income on rent, then 20\% of the remaining amount on food, and finally 50\% of the remaining amount on travelling. If the difference between the amount spent on travelling and the amount spent on rent is Rs. 13,000, what is his monthly income (in Rs.)?

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**Solution:**

1. Let the monthly income be $ x $.

2. Amount spent on rent = 10\% of $ x $ = $ 0.10x $.

3. Remaining amount after rent = $ x - 0.10x = 0.90x $.

4. Amount spent on food = 20\% of remaining = $ $0.20 \times 0.90x = 0.18x$ $.

5. Remaining amount after food = $ 0.90x - 0.18x = 0.72x $.

6. Amount spent on travelling = 50\% of remaining = $ $0.50 \times 0.72x = 0.36x$ $.

7. According to the problem, the difference between travelling and rent expenses is Rs. 13,000:

$$ 0.36x - 0.10x = 13000 $$

$$ 0.26x = 13000 $$

8. Solving for $ x $:

$$ $x = \frac{13000}{0.26} = 50000$ $$

**Answer:** Rs. 50,000

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