Interest - Study Mode
[#206] The simple interest on a certain sum of money at the rate of 5% per annum for 8 years is Rs. 840. Rate of interest for which the same amount of interest can be received on the same sum after 5 years is = ?
Correct Answer
(B) 8%
Explanation
Solution: $$eqalign{
& {x08f{Case - I:}} cr
& { ext{SI}}\% = { ext{R}}\% imes { ext{t}} cr
& { ext{SI}}\% = { ext{5}}\% imes { ext{8}} cr
& = { ext{40}}\% cr
& {x08f{Case - II:}} cr
& { ext{SI}}\% = { ext{5}} imes { ext{r}}\% { ext{ }} cr
& { ext{According to the question}} cr
& Rightarrow { ext{40}}\% = { ext{5}} imes { ext{r}}\% cr
& Rightarrow { ext{r}}\% = { ext{8}}\% cr} $$
[#207] If a sum of money double itself in 8 years, then the interest rate in percentage is ?
Correct Answer
(D) $$12frac{1}{2}$$ %
Explanation
Solution: Money is double itself means interest is equal to money. $$eqalign{
& { ext{P = }}frac{{{ ext{P}} imes { ext{8}} imes { ext{r}}}}{{100}} cr
& Rightarrow { ext{r = }}frac{{100}}{8} cr
& Rightarrow { ext{r = 12}}frac{1}{2}\% cr} $$
[#208] Alipta got some amount of money from her father. In how many years will the ratio of the money and the interest obtained from it be 10 : 3 at 6% simple interest per annum ?
Correct Answer
(C) 5 years
Explanation
Solution: $$eqalign{
& { ext{Let principal and SI is}} cr
& { ext{ = }}10x,{ ext{ }}3x{ ext{ }} cr
& { ext{and time is = }}t cr
& Rightarrow 3x = frac{{10x imes 6 imes t}}{{100}} cr
& Rightarrow t = 5,{ ext{years}} cr} $$
[#209] A sum of Rs. 3000 yields an interest of Rs. 1080 at 12% per annum simple interest in how many years ?
Correct Answer
(B) 3 years
Explanation
Solution: $$eqalign{
& { ext{By using formula }} cr
& Leftrightarrow frac{{{ ext{3000}} imes 12 imes { ext{T}}}}{{100}} = 1080 cr
& Leftrightarrow { ext{T = }}frac{{108}}{{36}}{ ext{ = 3 years}} cr} $$
[#210] A sum lent out at simple interest amounts to Rs. 6,076 in 1 year and
Rs. 7,504 in 4 years. The sum and the rate of interest p.a. are respectively:
Correct Answer
(B) Rs. 5,600 and 8.5%
Explanation
Solution: SI in three years = 7504 - 6076 = 1428 SI in one year $$ = frac{{1428}}{3} = 476$$ Now we can go through option
from option B $$frac{{5600 imes 8.5}}{{100}} = 476$$