By selling at Rs 77, some 2 1/4% shares of face-value Rs 100 and investing the proceeds in 6% shares of face value Rs 100, selling at Rs 110 a person increased his income by Rs 117 per annum. How many shares did he sell?

Two pipes running together can fill a cistern in 11 1/9 minutes. If one pipe takes 5 minutes more than the other to fill the cistern, find the time in which pipe would fill the cistern.

Please help me to find..

I am not familiar with the stock-market system in your country, but I can do the 2nd question

rate of first pipe = 1/x cisterns/min
rate of 2nd pipe = 1/(x+5) cisterns/min

combined rate = 1/x + 1/(x+5) = (x+5 + x)/(x(x+5))
but that is 11 1/9 min or 100/9 minutes

1/[(2x+5)/(x(x+5))] = 100/9
(2x+5)/(x(x+5)) = 9/100
9x^2 + 45x = 200x + 500
9x^2 - 155x - 500 = 0

it factors!
(x-20)(9x + 25) = 0
x = 20 or a negative, which is no good

so one pipe alone would take 20 minutes, the other 25 minutes

To solve this problem, let's break it down into steps:

Step 1: Find the profit made by selling each share
The profit made by selling each share can be calculated by subtracting the cost price from the selling price. In this case, the selling price is Rs 77 and the face value is Rs 100.
Profit per share = Selling price - Face value
Profit per share = Rs 77 - Rs 100 = -Rs 23 (negative sign represents loss)

Step 2: Calculate the number of shares sold
Let's assume the number of shares sold is x.
Total profit made by selling x shares = -Rs 23 * x

Step 3: Calculate the income from the new investment
The income from the new investment can be calculated by multiplying the number of shares purchased with the difference in selling price and face value.
Income from the new investment = Rs 117

Since the selling price of the new shares is Rs 110, the face value is Rs 100, and the annual income is Rs 117, using the formula:
Income from the new investment = (Selling price - Face value) * Number of shares purchased

Rs 117 = (Rs 110 - Rs 100) * Number of shares purchased
Rs 117 = Rs 10 * Number of shares purchased

Step 4: Set up and solve the equation
The total profit made by selling x shares is equal to the income from the new investment. Therefore:
-Rs 23 * x = Rs 10 * Number of shares purchased

We can solve this equation to find the value of x.

-Rs 23 * x = Rs 10 * Number of shares purchased
-Rs 23 * x = Rs 10 * (x / (2 1/4%))
-Rs 23 * x = Rs 10 * (x / (9/400))
-Rs 23 * x = Rs 10 * (x * 400/9)
-Rs 23 * x * 9 = Rs 10 * x * 400
-Rs 207 * x = Rs 4,000 * x
207 * x = 4,000 * x (ignoring the negative sign)

Dividing both sides by x:
207 = 4,000

But we have reached a contradiction, as there is no value for x that satisfies this equation. Therefore, there is no solution to this problem.

The problem might contain an error, or some information might be missing.

To solve these questions, we need to follow a step-by-step approach to find the answers.

1. Let's start with the first question about selling shares:

Step 1: Determine the selling price of the 2 1/4% shares.
The selling price is given as Rs 77.

Step 2: Determine the face value of the 2 1/4% shares.
The face value is given as Rs 100.

Step 3: Calculate the number of shares sold.
To do this, divide the selling price by the face value and multiply it by 100. In this case, (77 / 100) * 100 = 77 shares.

Step 4: Calculate the proceeds from selling these shares.
Multiply the number of shares sold by the selling price. In this case, 77 shares * Rs 77 = Rs 5,929.

Step 5: Determine the selling price of the 6% shares.
The selling price is given as Rs 110.

Step 6: Determine the face value of the 6% shares.
The face value is given as Rs 100.

Step 7: Calculate the number of shares bought with the proceeds.
To do this, divide the proceeds by the selling price and multiply it by 100. In this case, (5929 / 110) * 100 = 5,390 shares.

Step 8: Calculate the increase in income.
Subtract the income from the investment in 6% shares from the income from selling the 2 1/4% shares. In this case, Rs 117 - Rs 5,929 * 6% = Rs 117 - Rs 356.3 = Rs 760.7.

Step 9: Calculate the additional income per share.
Divide the additional income by the number of shares bought. In this case, Rs 760.7 / 5,390 shares = Rs 0.141 per share.

Step 10: Calculate the total shares sold.
To find the total shares sold, divide the additional income by the additional income per share. In this case, Rs 117 / Rs 0.141 = 829 shares.

Therefore, the person sold 829 shares.

Moving on to the second question:

Step 1: Determine the time taken by the two pipes together.
The time taken by the two pipes together is given as 11 1/9 minutes.

Step 2: Determine the time taken by the first pipe.
Let the time taken by the first pipe be x minutes.

Step 3: Determine the time taken by the second pipe.
Since the second pipe takes 5 minutes more than the first pipe to fill the cistern, the time taken by the second pipe is x + 5 minutes.

Step 4: Set up the equation.
Since the two pipes working together can fill the cistern in 11 1/9 minutes, we can set up the equation as follows:
1 / (x + x + 5) = 9 / 1

Step 5: Solve the equation.
To solve the equation, cross-multiply and simplify:
9(x + x + 5) = 1
18x + 45 = 1
18x = 1 - 45
18x = -44
x = (-44) / 18
x = -2.444

The time taken by the first pipe cannot be negative, so we discard this solution.

Therefore, there is no valid solution for the second question.

I hope this helps! Let me know if you have any further questions.

If he sold x shares, then he'd have made

.0214x

By selling them, he received 77x
Investing them, he bought

77x/100 shares of 6% shares.

77x/100 * .06 = .0462x

So, he increased his income by
(.0462-.0214)x = 117
x = Rs 4717.74

If the slow pipe takes x minutes, then we have

1/x + 1/(x+5) = 1/(11 1/9)
Now just solve for x and then x+5