Interest - Study Mode

[#11] The simple interest on a certain sum is one-eighth of the sum when the number of years is equal to half of the rate percentage per annum. Find the simple interest (in Rs.) on Rs. 15,000 at the same rate of simple interest for 8 years.
Correct Answer

(C) 6,000

Explanation

Solution: $$eqalign{
& { ext{Let sum}} = P cr
& frac{{P imes r imes t}}{{100}} = frac{1}{8}P cr
& rt = frac{{100}}{8} = frac{{25}}{2},.....,left( { ext{i}}
ight) cr
& { ext{Since }}t = frac{r}{2} cr
& { ext{From equation}}left( { ext{i}}
ight) cr
& r imes frac{r}{2} = frac{{25}}{2} cr
& r = 5\% cr
& { ext{If }}P = 1500 cr
& t = 8{ ext{ years}} cr
& { ext{S}}{ ext{.I}}{ ext{.}} = frac{{P imes r imes t}}{{100}} cr
& = frac{{15000 imes 8 imes 5}}{{100}} cr
& = { ext{Rs}}{ ext{. }}6,000 cr} $$

[#12] A person borrows Rs. 1,00,000 from a bank at 10% per annum simple interest and clears the debt in five years. If the instalment paid at the end of the first, second, third and fourth years to clear the debt are Rs. 10,000, Rs. 20,000, Rs. 30,000 and Rs. 40,000, respectively, what amount should be paid at the end of the fifth year to clear the debt?
Correct Answer

(B) Rs. 39,490

Explanation

Solution: $$eqalign{
& { ext{Interest at the end of }}{{ ext{1}}^{{ ext{st}}}}{ ext{ year}} cr
& = frac{{1,00,000 imes 10}}{{100}} cr
& = 10,000 cr
& { ext{Paid amount}} = 10,000 cr
& { ext{Rest amount}} cr
& = 1,10,000 - 10,000 cr
& = 1,00,000 cr
& { ext{Interest for }}{{ ext{2}}^{{ ext{nd}}}}{ ext{ year}} = 10,000 cr
& { ext{Amount paid}} = 20,000 cr
& { ext{Remaining amount}} cr
& = 1,10,000 - 20,000 cr
& = 90,000 cr
& { ext{Interest for }}{{ ext{3}}^{{ ext{rd}}}}{ ext{ year}} = 9,000 cr
& { ext{Amount paid}} = 30,000 cr
& { ext{Remaining amount}} cr
& = 99,000 - 30,000 cr
& = 69,000 cr
& { ext{Interest for }}{{ ext{4}}^{{ ext{th}}}}{ ext{ year}} = 6,900 cr
& { ext{Amount paid}} = 40,000 cr
& { ext{Remaining amount}} cr
& = 75,900 - 40,000 cr
& = 35,900 cr
& { ext{Interest for }}{{ ext{5}}^{{ ext{th}}}}{ ext{ year}} cr
& = frac{{35,900 imes 10}}{{100}} cr
& = 3,590 cr
& { ext{Amount paid at the end of }}{{ ext{5}}^{{ ext{th}}}}{ ext{ year}} cr
& = 35,900 + 3,590 cr
& = 39,490 cr} $$

[#13] A mobile phone is available for Rs. 25,000 or Rs. 5,200 down payment, followed by 4 equal monthly instalments. If the rate of interest is 25% p.a. simple interest, calculate the amount of each instalment.
Correct Answer

(D) Rs. 5,200

Explanation

Solution: $$eqalign{
& { ext{Cash payment}} = 25000 cr
& { ext{Down payment}} = 5200 cr
& { ext{Remaining}} = 19800 cr
& { ext{Installment}}left( x
ight) = 4 cr} $$ [x08egin{array}{*{20}{c}}
Rightarrow &{19800}&{ - x} \
{}&{19800}&{ - 2x} \
{}&{mathop {19800}limits_{\_\_\_\_\_\_\_\_\_\_\_} }&{mathop { - 3x}limits_{\_\_\_\_\_\_\_\_\_} } \
{}&{79200}&{ - 6x}
end{array}] $$eqalign{
& Rightarrow { ext{Interest}} = 4x - 19800 cr
& Rightarrow frac{{left( {79200 - 6x}
ight) imes 25}}{{12 imes 100}} = 4x - 19800 cr
& Rightarrow 1920x - 50400 = 79200 - 60x cr
& Rightarrow 1980x = 1029600 cr
& Rightarrow x = 5200 cr} $$

[#14] At which rate of simple interest does an amount become double in 12 years?
Correct Answer

(C) $$8frac{1}{3}\% $$

Explanation

Solution: $$eqalign{
& 1 = frac{{1 imes 12 imes r}}{{100}} cr
& r = 8frac{1}{3}\% cr} $$

[#15] On simple interest, a certain sum becomes Rs. 59,200 in 6 years and Rs. 72,000 in 10 years. If the rate of interest had been 2% more, then in how many years would the sum have become Rs. 76,000?
Correct Answer

(B) 9

Explanation

Solution: [x08egin{gathered}
Pxrightarrow{{{ ext{6 years}}}}59,200 hfill \
Pxrightarrow{{{ ext{10 years}}}}72,000 hfill \
end{gathered} ] $$eqalign{
& { ext{Difference 4 years}} cr
& = left( {72,000 - 59,200}
ight) cr
& = 12,800 cr
& { ext{1 year}} = frac{{12,800}}{4} = 3,200 cr
& herefore { ext{6 years S}}{ ext{.I}}{ ext{.}} cr
& = 3,200 imes 6 = 19,200 cr
& P = 59,200 - 19,200 = 40,000 cr
& { ext{S}}{ ext{.I}}{ ext{.}} = frac{{P imes r imes t}}{{100}} cr
& 19,200 = frac{{40,000 imes r imes 6}}{{100}} cr
& r = 8\% cr
& { ext{If }}r = 8\% + 2\% = 10\% cr
& P = 40,000 cr
& t = ? cr
& A = 76,000 cr
& herefore { ext{S}}{ ext{.I}}{ ext{.}} = 36,000 cr
& 36,000 = frac{{40,000 imes 10 imes t}}{{100}} cr
& t = 9{ ext{ years}} cr} $$