Interest - Study Mode
[#41] A person invests Rs. 12000 as fixed deposit at a bank at the rate of 10% per annum simple interest. But due to some pressing needs he has to withdraw the entire money after three years, for which the bank allowed him a lower rate of interest. If he gets Rs. 3320 less than what he would have got at the end of 5 years, the rate of interest allowed by the bank is = ?
Correct Answer
(B) $${ ext{7}}frac{4}{9}$$ %
Explanation
Solution: Principal = Rs. 12000 Rate % = 10% Interest paid by the person in 5 years $$eqalign{
& = frac{{12000 imes 10 imes 5}}{{100}} cr
& = { ext{Rs}}{ ext{. 6000}} cr} $$ Interest received by the person after 3 years $$eqalign{
& = { ext{Rs}}{ ext{. }}left( {6000 - 3320}
ight) cr
& = { ext{Rs}}{ ext{. 2680}} cr
& { ext{By using formula,}} cr
& { ext{Rate}}\% cr
& { ext{ = }}frac{{2680}}{{12000}} imes frac{{100}}{3} cr
& = frac{{67}}{9} cr
& = 7frac{4}{9}\% cr
& { ext{Hence required rate}}\% cr
& { ext{ = 7}}frac{4}{9}\% cr} $$
[#42] A certain scheme of investment in simple interest declares that it triples the investment in 8 years. If you want to quadruple the money through that scheme for how many years you have to invest for = ?
Correct Answer
(D) 12 years
Explanation
Solution: $$eqalign{
& { ext{P}} + frac{{P imes { ext{r}} imes { ext{t}}}}{{100}} = 3{ ext{P}} cr
& Rightarrow 1 + frac{{rt}}{{100}} = 3 cr
& Rightarrow frac{{{ ext{rt}}}}{{100}} = 2 cr
& Rightarrow { ext{r}} = frac{{2 imes 100}}{8} = 25\% cr
& { ext{so, }},left( {1 + frac{{{ ext{rt}}}}{{100}}}
ight) = 4 cr
& Rightarrow frac{{{ ext{rt}}}}{{100}} = 3 cr
& Rightarrow { ext{t}} = frac{{3 imes 100}}{{25}} cr
& Rightarrow { ext{t}} = 12,{ ext{years}} cr} $$
[#43] A person deposits Rs. 500 in 4 years and Rs. 600 for 3 years at the same rate of simple interest in a bank. Altogether he received Rs. 190 as interest. The rate of simple interest per annum was = ?
Correct Answer
(B) 5%
Explanation
Solution: Let rate of interest = R% According to the question, $$eqalign{
& frac{{500 imes 4 imes { ext{R}}}}{{100}} + frac{{600 imes 3 imes { ext{R}}}}{{100}} = 190 cr
& Rightarrow 20{ ext{R + 18R = 190}} cr
& Rightarrow 38{ ext{R = 190}} cr
& Rightarrow { ext{R = 5% }} cr} $$ Hence required rate % = 5% Alternate Note : In such type of questions to save your valuable time follow the given below method. Let rate of interest = 1% $$eqalign{
& { ext{Case (I): Interest (}}{{ ext{I}}_1}{ ext{)}} cr
& { ext{ = }}frac{{500 imes 4 imes 1}}{{100}} cr
& = 20 cr
& { ext{Case (II): Interest (}}{{ ext{I}}_2}{ ext{)}} cr
& { ext{ = }}frac{{{ ext{600}} imes 3 imes 1}}{{100}} cr
& = 18 cr} $$ According to the question, Interest Rate % 38 1 ↓×5 ↓×5 190 5% Hence required rate % = 5%
[#44] If the simple interest for 6 years be equal to 30% of the principal, it will be equal to the principal after
Correct Answer
(B) 20 years
Explanation
Solution: $$eqalign{
& { ext{Let sum}} = { ext{Rs}}{ ext{. }}x cr
& { ext{Then,}} cr
& { ext{S}}{ ext{.I}}{ ext{.}} = 30\% ,{ ext{of}},{ ext{Rs}}{ ext{.}},x cr
& ,,,,,,,,, = { ext{Rs}}{ ext{.}}frac{{3x}}{{10}} cr
& { ext{Time}} = 6,{ ext{years}}{ ext{.}} cr
& herefore { ext{Rate}} = left( {frac{{100 imes 3x}}{{10 imes x imes 6}}}
ight)\% cr
& ,,,,,,,,,,,,,,,,, = 5\% cr
& { ext{Now, sum}} = { ext{Rs}}{ ext{. }}x cr
& { ext{S}}{ ext{.I}}{ ext{.}} = { ext{Rs}}{ ext{. }}x cr
& { ext{Rate}} = 5\% cr
& herefore { ext{Time}} = left( {frac{{100 imes x}}{{x imes 5}}}
ight){ ext{years}} cr
& ,,,,,,,,,,,,,,,,,, = 20,{ ext{years}} cr} $$
[#45] Simple interest on a certain sum at a certain annual rate of interest is $$frac{1}{9}$$ of the sum. If the numbers representing rate percent and time in years be equal, then the rate of interest is -
Correct Answer
(A) $$3frac{1}{3}$$ %
Explanation
Solution: $$eqalign{
& { ext{Let sum}} = x cr
& { ext{Then,}} cr
& { ext{S}}{ ext{.I}}{ ext{.}} = frac{x}{9}. cr
& { ext{Let rate}} = { ext{R}}\% ,{ ext{and}} cr
& { ext{time}} = { ext{R}},{ ext{years}}{ ext{.}} cr
& herefore left( {frac{{x imes { ext{R}} imes { ext{R}}}}{{100}}}
ight) = frac{x}{9} cr
& Rightarrow {{ ext{R}}^2} = frac{{100}}{9} cr
& Rightarrow { ext{R}} = frac{{10}}{3} = 3frac{1}{3} cr
& { ext{Hence, rate}} = 3frac{1}{3}\% cr} $$