Interest - Study Mode
[#201] A certain sum doubles in 7 years at simple interest. The same sum under the same interest rate will become 4 times in how many years = ?
Correct Answer
(C) 21 years
Explanation
Solution: $$eqalign{
& frac{{left( {n - 1}
ight)}}{{{t_1}}} = frac{{left( {m - 1}
ight)}}{{{t_2}}} cr
& frac{1}{7} = frac{3}{{{t_2}}} cr
& {t_2} = 21{ ext{ years}} cr} $$
[#202] On a certain sum the simple interest for $$12frac{1}{2}$$ year is $$frac{3}{4}$$ of the sum. Then the rate of interest is = ?
Correct Answer
(B) 6% per year
Explanation
Solution: $$eqalign{
& { ext{Let sum = }}x cr
& { ext{Interest = }}frac{3}{4}x{ ext{ }} cr
& { ext{Interest = }}frac{{{ ext{PTR }}}}{{100}} cr
& Rightarrow frac{3}{4}x = frac{{x imes { ext{R}} imes 12.5}}{{100}} cr
& { ext{R = 6}}\% cr} $$
[#203] If the simple interest on Rs. 1 for 1 month is 1 paisa, then the rate percent per annum will be = ?
Correct Answer
(C) 12%
Explanation
Solution: $$eqalign{
& { ext{t}} = { ext{1 month = }}frac{1}{{12}}{ ext{year}} cr
& { ext{SI = 1 paisa = Rs}}{ ext{. }}frac{1}{{100}} cr
& { ext{r}}\% = frac{{{ ext{SI}} imes { ext{100}}}}{{{ ext{P}} imes { ext{T}}}} = frac{{1 imes 100 imes 12}}{{100 imes 1 imes 1}} cr
& { ext{r}}\% = 12\% cr} $$
[#204] A person invests money in three different schemes for 6 years, 10 years and 12 years at 10 percent, 12 percent and 15 percent simple interest respectively. At the completion of each scheme, he gets the same interest. The ratio of his investment is
Correct Answer
(D) 6 : 3 : 2
Explanation
Solution: Let the three amounts be Rs. x, Rs. y and Rs. z, Then, $$eqalign{
& frac{{x imes 10 imes 6}}{{100}} = frac{{y imes 12 imes 10}}{{100}} = frac{{z imes 15 imes 12}}{{100}} cr
& Rightarrow 60x = 120y = 180z cr
& Rightarrow x = 2y = 3z = k(say) cr
& Rightarrow x = k,y = frac{k}{2},z = frac{k}{3} cr
& Rightarrow x:y:z = k:frac{k}{2}:frac{k}{3} cr
& Rightarrow x:y:z = 1:frac{1}{2}:frac{1}{3} cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,, = 6:3:2 cr} $$
[#205] Find the amount to be received after 2 years 6 months at the rate of 5% p.a. of simple interest on a sum of Rs. 3200.
Correct Answer
(C) Rs. 3600
Explanation
Solution: $$eqalign{
& { ext{Rate of interest}} = { ext{5}}\% { ext{ p}}{ ext{.a}}{ ext{.}} cr
& { ext{sum}} = { ext{Rs}}{ ext{. 3200}} cr
& { ext{Time}} = { ext{2 years 6 months}} cr
& ,,,,,,,,,,,,,,, = 2frac{1}{2}{ ext{years}} cr
& ,,,,,,,,,,,,,,, = frac{5}{2}{ ext{years}} cr
& { ext{S}}{ ext{.I}}{ ext{.}} = frac{{{ ext{Prinicipal}} imes { ext{Time}} imes { ext{Rate}}}}{{100}} cr
& ,,,,,,,,,, = frac{{3200 imes 5 imes 5}}{{2 imes 100}} cr
& ,,,,,,,,,, = { ext{Rs}}{ ext{. }}400 cr
& herefore { ext{Amount}} = { ext{Rs}}{ ext{. sum}} + { ext{S}}{ ext{.I}}. cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,,, = left( {3200 + 400}
ight) cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,,, = { ext{Rs}}{ ext{. 3600}}{ ext{}} cr} $$