Question

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..

Answer 1

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

Answer 2

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