The monthly income of A is Rs. 50000. He spends *x*\% of his monthly income on rent. From the remaining amount, he spends 20\% on his children's education, and then half of the remaining amount on travelling. If A saves Rs. 18000, find by what percent the amount spent on travelling is more than the amount spent on rent.

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**Solution:**

1. Let the monthly income be Rs. 50000.

2. A spends *x*\% on rent, so rent amount = $ \frac{x}{100} \times 50000 = 500x $.

3. Remaining income after rent = $ 50000 - 500x $.

4. He spends 20\% of the remaining on children's education:
   $$ \text{Education} = 0.20 \times (50000 - 500x) = 10000 - 100x $$

5. Remaining after education = $ (50000 - 500x) - (10000 - 100x) = 40000 - 400x $.

6. He spends half of this remaining on travelling:
   $$ \text{Travelling} = \frac{1}{2} \times (40000 - 400x) = 20000 - 200x $$

7. The amount saved is Rs. 18000, so:
   $$ \text{Savings} = \text{Income} - (\text{Rent} + \text{Education} + \text{Travelling}) $$
   $$ 18000 = 50000 - (500x + 10000 - 100x + 20000 - 200x) $$

8. Simplify the sum inside the parenthesis:
   $$ 500x + 10000 - 100x + 20000 - 200x = (500x - 100x - 200x) + (10000 + 20000) = 200x + 30000 $$

9. So,
   $$ 18000 = 50000 - (200x + 30000) $$
   $$ 18000 = 20000 - 200x $$

10. Rearranging:
    $$ 200x = 20000 - 18000 = 2000 $$
    $$ x = \frac{2000}{200} = 10 $$

11. Rent amount = $ 500 \times 10 = 5000 $

12. Travelling amount = $ 20000 - 200 \times 10 = 20000 - 2000 = 18000 $

13. Find the percentage by which travelling is more than rent:
    $$ \frac{18000 - 5000}{5000} \times 100 = \frac{13000}{5000} \times 100 = 260\% $$

**Answer:** 260\%

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