Remark : The day on which money is deposited is not counted while the day on which money is withdrawn is counted .
Ex. 3. A sum at simple interests at 13 ½ % per annum amounts to Rs.2502.50 after 4 years find the sum.
Sol.Let sum be Rs. x then , S.I.=Rs.(x*(27/2) *4*(1/100) ) = Rs.27x/50
\amount = (Rs. x+(27x/50)) = Rs.77x/50
\ 77x/50 = 2502.50 Û x = 2502.50 * 50= 1625
77
Hence , sum = Rs.1625.
Ex. 4. A sum of Rs. 800 amounts to Rs. 920 in 8 years at simple intere
interest rate is increased by 8%, it would amount to bow mucb ?
Sol. S.l. = Rs. (920 - 800) = Rs. 120; p = Rs. 800, T = 3 yrs. _
. R = ((100 x 120)/(800*3) ) % = 5%.
New rate = (5 + 3)% = 8%.
New S.l. = Rs. (800*8*3)/100 = Rs. 192.
:New amount = Rs.(800+192) = Rs. 992.
Ex. 5. Adam borrowed some money at the rate of 6% p.a. for the first two years , atthe rate of 9% p.a. for the next three years , and at the rate of 14% p.a. for the period beyond five years. 1£ he pays a total interest of Rs. 11, 400 at the end of nine years how much money did he borrow ?
Sol. Let the sum borrowed be x. Then,
(x*2*6)/100 + (x*9*3)/100 + (x*14*4)/100 = 11400
Û(3x/25 + 27x/100 + 14x / 25) = 11400Û 95x/100 = 11400 Û x = (11400*100)/95 = 12000.
Hence , sumborrowed = Rs.12,000.
Ex. 6. A certain sum of money amounts to Rs. 1008 in 2 years and to Rs.1164 in 3 ½ years. Find the sum and rate of interests.
Sol.. S.I. for 1 ½ years = Rs.(1164-1008) = Rs.156.
S.l. for 2 years = Rs.(156*(2/3)*2)=Rs.208
Principal = Rs. (1008 - 208) = Rs. 800.
Now, P = 800, T = 2 and S.l. = 208.
Rate =(100* 208)/(800*2)% = 13%
Ex. 7. At what rate percent per annum will a sum of money double in 16 years.
Sol.. Let principal = P. Then, S.l. = P and T = 16 yrs.
\Rate = (100 x P)/(P*16)% = 6 ¼ % p.a.
Ex. 8. The simple interest on a sum of money is 4/9 of the principal .Find the rate percent and time, if both are numerically equal.
Sol. Let sum = Rs. x. Then, S.l. = Rs. 4x/9
Let rate = R% and time = R years.
Then, (x*R*R)/100=4x/9 or R2 =400/9 or R = 20/3 = 6 2/3.
\Rate = 6 2/3 % and Time = 6 2/3 years = 6 years 8 months.
Ex. 9. The simple interest on a certain sum of money for 2 l/2 years at 12% per
annumis Rs. 40 less tban the simple interest on the same sum for 3 ½years at 10% per annum. Find the sum.
Sol.Let the sum be Rs. x Then, ((x*10*7)/(100*2)) – ( (x*12*5)/(100*2)) = 40
Û (7x/20)-(3x/10)=40
Ûx = (40 * 20) = 800.
Hence, the sum is Rs. 800.
Ex. 10. 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.
Sol. Let sum = P and original rate = R.
Then, [ (P*(R+2)*3)/100] – [ (P*R*3)/100] = 360.
Û 3PR + 6P - 3PR = 36000 Û 6P=36000 Û P=6000
Hence, sum = Rs. 6000.
Ex. 11. What annual instalment will discharge a debt of Rs. 1092 due in 3 years