Ravi had 6 coins in his wallet as shown. He took out only 4 coins to pay the exact amount for a bun. Which of the following amounts is not a possible cost of the bun?

1. List the available coins and their values

The available coins are: $5\text{c}, 5\text{c}, 10\text{c}, 20\text{c}, 50\text{c}, \char36{}1$. In dollars, these are $\char36{}0.05, \char36{}0.05, \char36{}0.10, \char36{}0.20, \char36{}0.50, \char36{}1.00$.

2. Check if option (1) $1.65 is possible with exactly 4 coins

To make $\char36{}1.65$, we can use: $\char36{}1.00 + \char36{}0.50 + \char36{}0.10 + \char36{}0.05 = \char36{}1.65$. This uses exactly 4 coins. So $\char36{}1.65$ is possible.

3. Check if option (3) $1.35 is possible with exactly 4 coins

To make $\char36{}1.35$, we can use: $\char36{}1.00 + \char36{}0.20 + \char36{}0.10 + \char36{}0.05 = \char36{}1.35$. This uses exactly 4 coins. So $\char36{}1.35$ is possible.

4. Check if option (4) $1.30 is possible with exactly 4 coins

To make $\char36{}1.30$, we can use: $\char36{}1.00 + \char36{}0.20 + \char36{}0.05 + \char36{}0.05 = \char36{}1.30$. This uses exactly 4 coins. So $\char36{}1.30$ is possible.

5. Check if option (2) $1.40 is possible with exactly 4 coins

To make $\char36{}1.40$, we must use the $\char36{}1.00$ coin (otherwise the maximum with 4 coins is $0.50+0.20+0.10+0.05 = \char36{}0.85$). We need $\char36{}0.40$ more from 3 coins. The remaining coins are $50\text{c}, 20\text{c}, 10\text{c}, 5\text{c}, 5\text{c}$. We cannot make exactly $40\text{c}$ with 3 of these coins (e.g., $20+10+5=35$, $20+10+10$ is not possible as there is only one $10\text{c}$ coin). Thus, $\char36{}1.40$ is not possible.