Explanation:

- Let's assume Chetan has \( C \) coins.

- Gaurav has 40% more coins than Chetan. So, Gaurav has \( C + 0.4C = 1.4C \) coins.

- Avinash has 20% less coins than Gaurav. So, Avinash has \( 1.4C - 0.2 \times 1.4C = 1.12C \) coins.

To find by what percent the number of coins Chetan has is less than Avinash's, use the formula:

$$

\frac{\text{Avinash's coins} - \text{Chetan's coins}}{\text{Avinash's coins}} \times 100

= \frac{1.12C - C}{1.12C} \times 100 = \frac{0.12C}{1.12C} \times 100 = \frac{0.12}{1.12} \times 100 \approx 10.7\%

$$

- Option 1: 10.7 is correct.

- Option 2: 10.6 is incorrect.

- Option 3: 10.5 is incorrect.

- Option 4: 12 is incorrect.

Hence, the correct answer is $$ \color{green}{\checkmark} $$ 10.7.

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