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.

Question:Simple interest on a certain sum is `16/25` of the sum. Find the rate percent and time, If both are numerically equal. 

Let sum = x. Then, S.I = `(16x)/25`

Let rate = R % and time = R years.

`:. (x xx R xx R)/(100)`

`= (16x)/25 or R^2 = (1600)/25 R = 40/5 = 8`

:. Rate = 8% and Time = 8 years.

Question:A man borrowed Rs 24000 from two money Ienders. For one loan, he paid 15% per annum and for the other 18% per annum. At the end of one year, he paid Rs. 4050. How much did he borrow at each rate ? 

Let the sum at 15% be Rs x and that at 18% be Rs (24000 - x).

`:. (x xx 15 xx 1)/(100) + ((24000 - x) xx 18 xx 1)/(100)`

`= 4050`

`or 15x + 432000 - 18x`

`= 405000 or x = 9000.`

:. Money borrowed at 18% = Rs. 15000.

Question:What annual installment will discharge a debt of Rs 1092 due in 3 years at 12% simple interest ? 

Let each installment be Rs. x. then

`(x + (x xx 12 xx 1)/(100)) + (x + (x xx 12 xx 2)/(100)) + x`

`= 1092`

`or (28x)/25 + (31x)/25 + x`

`= 1092 or (28x + 31x + 25x)`

`= (1092 xx 25)`

`or x = ((1092 xx 25)/(84))`

`= 325.`

:. Each installment = Rs. 325