The cost price of a chair is 25% less than the cost price of a table. If a man sells 5 chairs at the cost price of 7 tables, what is his profit per cent?

The correct option is 86.66.

To find the profit percent, let us break down the relation between the cost prices and the selling prices step-by-step.

Step 1: Define the cost price of a table and a chair
Let the cost price (CP) of a table be $T$.
The cost price of a chair ($C$) is 25% less than the cost price of a table. Therefore, we can express the cost price of a chair as:
$C=T-0.25T=0.75T$
This means the total cost price of 5 chairs is:
$\text{Total Cost Price (CP)}=5\times 0.75T=3.75T$

Step 2: Determine the selling price of 5 chairs
According to the problem, the man sells 5 chairs at the cost price of 7 tables. Therefore:
$\text{Total Selling Price (SP)}=7T$

Step 3: Calculate the profit
Profit is the difference between the total selling price and the total cost price of the 5 chairs:
$\text{Profit}=\text{Total SP}-\text{Total CP}$
Substituting the values:
$\text{Profit}=7T-3.75T=3.25T$

Step 4: Calculate the profit percent
The profit percent is calculated based on the total cost price of the chairs:
$\text{Profit Percent}=\frac{\text{Profit}}{\text{Total CP}}\times 100$
Substituting the expressions we found:
$\text{Profit Percent}=\frac{3.25T}{3.75T}\times 100$
We can simplify the expression by canceling out $T$ and rewriting the decimals as integers:
$\text{Profit Percent}=\frac{3.25}{3.75}\times 100=\frac{325}{375}\times 100$
Reducing the fraction by dividing the numerator and the denominator by 25:
$\text{Profit Percent}=\frac{13}{15}\times 100=\frac{1300}{15}\approx 86.66\%$

Thus, the man's profit percentage is 86.66%.