Interest - Study Mode

[#216] A sum becomes 4 times at simple interest in 10 years. What is the rate of interest?
Correct Answer

(C) 30%

Explanation

Solution: $$eqalign{
& {1^{{ ext{st}}}},{ ext{Method}}: cr
& { ext{Let rate is }}R\% cr
& { ext{Now}}, cr
& P = 100, cr
& A = 400, cr
& I = 400 - 100 = 300, cr
& { ext{Time}},,T = 10,{ ext{years}} cr
& I = frac{{PTR}}{{100}} cr
& { ext{Or}},R = frac{{ {100 imes I} }}{{PT}} cr
& { ext{Or}},R = frac{{ {100 imes 300} }}{{ {100 imes 10} }} cr
& { ext{Hence}},{kern 1pt} R = 30\% cr} $$ 2 nd Method : Here, the sum become 4 times that means 100, become 400. Rate of such question is given by $$R = frac{{{ ext{interest}}}}{{{ ext{time}}}} = frac{{300}}{{10}} = 30\% $$ 3 rd Method : Here, 300% of rise in the sum so $$eqalign{
& 100 - - - 300\% uparrow - - - {kern 1pt} 400
cr
& R = {frac{{{ ext{total}},{ ext{percentage rise}}}}{{{ ext{given time}}}}} cr
& ,,,,,,,, = frac{{300\% }}{{10}} cr
& ,,,,,,,, = 30\% cr} $$

[#217] If a certain sum of money becomes doubles at simple interest in 12 years, what would be the rate of interest per annum?
Correct Answer

(A) $$8frac{1}{3}$$

Explanation

Solution: Let,
Principal, P = Rs. 100
Amount, A = Rs. 200
Time = 12 years
Interest = Rs. 100
Rate of interest $$eqalign{
& = frac{{{ ext{Total Interest}}}}{{{ ext{Given Time}}}} cr
& = frac{{100}}{{12}} cr
& = 8frac{1}{3}\% cr} $$

[#218] An amount of Rs. 1,00,000 is invested in two types of shares. The first yields an interest of 9% p.a. and second, 11% p.a. If the total interest at the end of one year is $$9frac{3}{4}$$ %, then the amount invested in each share was -
Correct Answer

(B) Rs. 62, 500 Rs. 37, 500

Explanation

Solution: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then, $$eqalign{
& = left( {frac{{x imes 9 imes 1}}{{100}}}
ight) + left[ {frac{{left( {100000 - x}
ight) imes 11 imes 1}}{{100}}}
ight] cr
& = left( {100000 imes frac{{39}}{4} imes frac{1}{{100}}}
ight) cr
& Leftrightarrow frac{{9x + 1100000 - 11x}}{{100}} = frac{{39000}}{4} = 9750 cr
& Leftrightarrow 2x = left( {1100000 - 975000}
ight) = 125000 cr
& Leftrightarrow x = 62500 cr
& herefore { ext{Sum invested at 9}}\% cr
& = { ext{Rs}}{ ext{. }}62500 cr
& { ext{Sum invested at 11% }} cr
& { ext{ = Rs}}{ ext{.}}left( {100000 - 62500}
ight) cr
& = { ext{Rs}}{ ext{. }}37500 cr} $$