by selling at 77% some 9/4%shares of face value 100 and investing the proceeds in 6% shares of face value 100, selling at 110 a person got profit of 117. how many shares did he sell?

To solve this problem, let's break it down step-by-step:

Step 1: Calculate the selling price of the 9/4% shares
The selling price of the 9/4% shares is given as 77% of their face value. To calculate the selling price, we can use the formula:
Selling Price = Face Value * (Selling Percentage/100)
Selling Price = 100 * (77/100)
Selling Price = 77

Step 2: Calculate the number of 9/4% shares sold
Let's assume the number of 9/4% shares sold is "x."
Therefore, the total proceeds from selling the 9/4% shares can be calculated as:
Total Proceeds = Selling Price * Number of Shares Sold
117 = 77 * x

Step 3: Calculate the cost of the new 6% shares
The proceeds from selling the 9/4% shares are then invested in 6% shares. The cost of the 6% shares is given as:
Cost of Shares = Selling Price * Number of Shares Sold
Cost of Shares = 110 * x

Step 4: Calculate the profit
Profit = Cost of New Shares - Total Proceeds
117 = (110 * x) - (77 * x)

Step 5: Solve for x
117 = 110x - 77x
117 = 33x
x = 117 / 33
x = 3.545

Since shares cannot be in decimal places, we can round down to the nearest whole number:
x ≈ 3

Therefore, he sold approximately 3 shares.

To solve this problem, let's break it down step by step.

1. Let's assume the person sold 'x' shares of the first type, which are sold at 77% of their face value (100).
So, the total amount received from selling the first type of shares is x * (77/100) * 100 = 77x.

2. The person invested the proceeds in the second type of shares, which are sold at face value (100) at a profit of 110.
So, the total amount received after investing is 77x * (110/100) = 84.7x.

3. The person made a profit of 117, which means the total amount received after investing minus the total amount invested is equal to 117.
Hence, we have the equation: 84.7x - 77x = 117.

4. Solving the equation: 7.7x = 117.
Dividing both sides by 7.7, we get x = 15.

Therefore, the person sold 15 shares of the first type.