Interest - Study Mode

[#186] A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6$$frac{1}{4}$$ p.a for 2 years. Find his gain in the transaction per year.
Correct Answer

(A) Rs. 112.50

Explanation

Solution: $${ ext{Gain in 2 years}}$$ $$ = { ext{Rs}}{ ext{.}},left[ {left( {5000 imes frac{{25}}{4} imes frac{2}{{100}}}
ight) - left( {frac{{5000 imes 4 imes 2}}{{100}}}
ight)}
ight]$$ $$eqalign{
& = { ext{Rs}}{ ext{.}},left( {625 - 400}
ight) cr
& = { ext{Rs}}.225 cr
& herefore { ext{Gain in 1 year}} cr
& = { ext{Rs}}{ ext{.}},left( {frac{{225}}{2}}
ight) cr
& = { ext{Rs}}{ ext{.}},112.50 cr} $$

[#187] A sum of money becomes $$frac{7}{6}$$ of itself in 3 years at a certain rate of simple interest. The rate of interest per annum is ?
Correct Answer

(A) $$5frac{5}{9}$$ %

Explanation

Solution: $$eqalign{
& { ext{Let principal = 6P}} cr
& { ext{Hence Amount}} cr
& { ext{ = 6P}} imes frac{7}{6} = 7{ ext{P}} cr
& herefore { ext{SI = 7P}} - { ext{6P = P}} cr
& { ext{Time = 3 years}} cr
& x08oxed{{ ext{SI = }}frac{{{ ext{P}} imes { ext{T}} imes { ext{R}}}}{{100}}} cr
& Rightarrow { ext{P = }}frac{{6{ ext{P}} imes { ext{R}} imes { ext{3}}}}{{100}} cr
& Rightarrow { ext{R = }}frac{{100}}{{18}} cr
& ,,,,,,,,,,,, = frac{{50}}{9} cr
& ,,,,,,,,,,,, = 5frac{5}{9}\% cr} $$ Alternate: Note: In such type of questions to save your valuable time try to think like that. [x08egin{gathered}
x08egin{array}{*{20}{c}}
{{ ext{Amount}}}&{{ ext{Principal}}}
end{array} hfill \
{ ext{ }}underbrace {7,,,,,,,,,,,,,,,,,,,,,,,,,,,,{ ext{6}}}_{ + 1} hfill \
end{gathered} ] $$eqalign{
& { ext{Required rate % }} cr
& { ext{ = }}frac{1}{6} imes frac{{100}}{3} cr
& = 5frac{5}{9}\% cr} $$

[#188] The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rates of interest is ?
Correct Answer

(C) 0.3%

Explanation

Solution: Let the rate of interest for two different sources is r 1 and r 2 respectively. $$eqalign{
& frac{{1500 imes {{ ext{r}}_1} imes 3}}{{100}} - frac{{1500 imes {{ ext{r}}_2} imes 3}}{{100}} cr
& = 13.50 cr
& 4500{{ ext{r}}_1} - 4500{{ ext{r}}_2} = 1350 cr
& left( {{{ ext{r}}_1} - {{ ext{r}}_2}}
ight) = frac{{1350}}{{4500}} = 0.3\% cr} $$ Hence required difference in rates = 0.3%

[#189] A sum of Rs. 1600 gives a simple interest of Rs. 252 in 2 years and 3 months. The rate of interest per annum is = ?
Correct Answer

(C) 7 %

Explanation

Solution: $$eqalign{
& { ext{Time = 2 years 3 months}} cr
& { ext{ = 2 + }}frac{3}{{12}}{ ext{ = }}frac{9}{2}{ ext{ years}} cr
& { ext{We know }}x08oxed{{ ext{SI = }}frac{{{ ext{P}} imes { ext{T}} imes { ext{R}}}}{{100}}} cr
& { ext{P = Rs 1600,}} cr
& { ext{T = }}frac{9}{4}{ ext{years,}} cr
& { ext{SI = Rs 252}} cr
& { ext{Put values in the formula ,}} cr
& Rightarrow 252 = frac{{1600 imes { ext{R}} imes 9}}{{100}} cr
& Rightarrow 252 = 36{ ext{R}} cr
& Rightarrow { ext{R = }}frac{{252}}{{36}} = 7\% cr} $$

[#190] Ram borrows Rs. 520 from Gaurav at a simple interest of 13% per annum. What amount of money should Ram pay to Gaurav after 6 months to be absolved of the debt?.
Correct Answer

(D) Rs. 553.80

Explanation

Solution: $$eqalign{
& { ext{P}} = { ext{Rs}}.,520, cr
& { ext{R}} = 13\% cr
& { ext{T}} = frac{1}{2}yr. cr
& herefore { ext{S}}{ ext{.I}}{ ext{.}} = { ext{Rs}}{ ext{.}}left( {frac{{520 imes 13}}{{100 imes 2}}}
ight) cr
& ,,,,,,,,,,,,,, = { ext{Rs}}{ ext{. }}33.80 cr
& { ext{Hence, amount after 6 months}} cr
& = { ext{Rs}}{ ext{. }}left( {520 + 33.80}
ight) cr
& = { ext{Rs}}{ ext{. }}553.80 cr} $$