An employee spends 20\% of his salary on rent. From the remaining amount, he gives 10\% to his grandmother. Then, he spends 30\% of the remaining amount on food. The rest of the salary is saved. What is the ratio of his savings to his total expenditure?

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**Solution:**

1. Let the total salary be $100$ units.

2. Rent expenditure = 20\% of salary = $20$ units.

3. Remaining salary after rent = $100 - 20 = 80$ units.

4. Amount given to grandmother = 10\% of remaining = 10\% of $80 = 8$ units.

5. Remaining after giving to grandmother = $80 - 8 = 72$ units.

6. Food expenditure = 30\% of remaining = 30\% of $72 = 21.6$ units.

7. Remaining amount (savings) = $72 - 21.6 = 50.4$ units.

8. Total expenditure = Rent + Given to grandmother + Food = $20 + 8 + 21.6 = 49.6$ units.

9. Ratio of savings to expenditure = $50.4 : 49.6$.

10. Multiply both terms by 10 to avoid decimals: $504 : 496$.

11. Simplify the ratio by dividing both by 8:
    - $504 \div 8 = 63$
    - $496 \div 8 = 62$

**Answer:** $63 : 62$

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