Question:Find the annual income by investing Rs. 6800 in 10% stock at 136. 

By investing Rs.136, income obtained = Rs. 10

By investing Rs. 6800, income obtained` = Rs. (10/136 xx 6800)`

   `= Rs. 500`

Question:Which is better investment ?

`7 1/2%` stock at 105 or `6 1/2%` stock at 94. 

Let the investing in each case be Rs.`(105 xx 94).`

 Case I : `7 1/2%` stock at 105 :

 On investing Rs. 105, income` = Rs. 15/2`

 On investing Rs. `(105 xx 94),` income

`= Rs. (15/2 xx 1/105 xx 105 xx 94)`

`= Rs. 705.`

  Case II :` 6 1/2%` stock at 94 :

  On investing Rs. 94, income` = Rs. 13/2`

  On investing Rs.`( 105 xx 94)`, income

  `= Rs. (13/2 xx 1/94 xx 105 xx 94)`

  `= Rs. (1365)/2`

  `= Rs. 682.50.`

  Clearly, the income from` 7 1/2%` stock at 105 is more.

  Hence, the investment in` 7 1/2%` stock at 105 is better.

Question:Find the cost of 96 shares of Rs. 10 each at` 3/4` discount, brokerage being` 1/4` per share. 

Cost of 1 share

` = Rs. [(10 - 3/4) + 1/4]`

 `= Rs. 19/2.`

 Cost of 96 shares 

`= Rs. (19/2 xx 96)`

`= Rs. 912.`

Question:Find the income derived from 88 shares of Rs.25 each at 5 premium, brokerage being `1/4` per share and the rate of dividend being `7 1/2`% per annum. Also, find the rate of interest on the investment. 

Cost of 1 share` = Rs. (25 + 5 + 1/4)`

                      `= Rs. 121/4`

Cost of 88 shares` = Rs.(121/4 xx 88)`

                           `= Rs. 2662.`

:. Investment made` - Rs. 2662.`

Face value of 88 shares` = Rs. (88 xx 25)`

                                    `= Rs. 2200.`

Dividend on Rs.` 100 = 15/2.`

Dividend on Rs. 2200` = Rs. (15/2 xx 1/100 xx 2200)`

                                  `= Rs. 165.`

:. Income derived = Rs. 165.

Rate of interest on investment` = (165/2662 xx 100)`

                                           `= 6.2 %`.

Question:A man buys Rs. 25 shares in a company which pays 9% dividend. The money invested is such that it gives 10% on investment. At what price did he buy the shares ? 

Suppose he buys each share for Rs. x.

Then,` (25 xx 9/100) = (x xx 10/100) or x = 22.50.`

:. Cost of each share = Rs. 22.50.

Question:10. A man sells Rs. 5000, 12% stock at 156 and invests the proceeds party in 8% stock at 90 and 9% stock at 108. He thereby increase his income by Rs. 70. How much of the proceeds were investing in each stock ? 

S.P. of Rs. 5000 stock`= Rs. (156/100 xx 5000)`

            `= Rs. 7800.`

Income from this stock` = Rs. (12/100 xx 5000)`

         `= Rs. 600.`

Let investment in 8% stock be x & that in 9% stock = (7800 - x).

`:. (x xx 8/90) + (7800 - x) xx 9/108 = (600 + 70)`

`or 4x/45 + (7800 - x)/12`

`= 670`

`or 16x + 117000 - 15x`

`= (670 xx 180) or x = 3600.`

:. Money invested in 9% stock at 108 

`= Rs. (7800 - 3600)`

`= Rs. 4200.`

Question:A sum at simple interest at` 13 1/2%` per annum amounts to Rs. 2502.50 after 4 years. Find the sum. 

Let sum be x. Then,

S.I.` =(x xx 27/2 xx 4 xx 1/100)`

    `= (27x)/50`

:. Amount` = (x + (27x)/50)`

              `= (77x)/50`

`:. (77x)/50 = 2502.50 or x`

`= (2502.50 xx 50)/(77)`

`= 1625`

Hence, sum = Rs. 1625

Question:A certain sum of money amounts to Rs. 1008 in 2 years and to Rs 1164 in` 3 2/1` years. Find the sum and the rate of interest. 

S.I. for` 1 1/2` years = Rs. (1164 - 1008) = Rs 156.

S.I. for 2 years` = Rs.(156 xx 2/3 xx 2) = Rs. 208`

:. principal` = Rs. (1008 - 208) = Rs. 800`

Now, P = 800, T = 2 and S.I. = 208

:. Rate` = ((100 xx S.I)/(P xx T))`

  `= ((100 xx 208)/(800 xx 2))%`

` = 13%`

Question:At what rate percent per annum will a sum of money double in 8 years ? 

Let principal = P. Then, S.I. = P and Time = 8 years .

:. Rate` = ((100 xx P)/(P xx 8))%`

  `= 12.5%` per annum.

Question:A sum was put at simple interest at a certain rate for 3 years. Had it been put at 2% higher rate, it would have fetched Rs. 360 more. Find the sum. 

Let sum = P and original rate = R. Then,

`(P xx (R + 2) xx 3)/(100) - (P xx R xx 3)/(100)`

`= 360`

or 3 PR + 6P - 3PR

`= 36000 or 6P`

`= 36000 or P = 6000.

Hence, sum = Rs 6000.