Interest - Study Mode

[#1] Asmita invest an amount of Rs. 9534 @ 4 p.c.p.a to obtain a total amount of Rs. 11442 on simple interest after a certain period. For how many years did she invest the amount to obtain the total sum?
Correct Answer

(C) 5 years

Explanation

Solution: $$eqalign{
& { ext{P}} = { ext{Rs}}{ ext{. 9534}} cr
& { ext{S}}{ ext{.I}}{ ext{.}} = { ext{Rs}}{ ext{.}}left( {{ ext{11442}} - { ext{9534}}}
ight) cr
& ,,,,,,,,, = { ext{Rs}}{ ext{.1908}} cr
& { ext{R}} = { ext{4}}\% cr
& herefore { ext{Time}} = left( {frac{{{ ext{100}} imes { ext{1908}}}}{{{ ext{9534}} imes { ext{4}}}}}
ight){ ext{years}} cr
& = left( {frac{{{ ext{47700}}}}{{{ ext{9534}}}}}
ight){ ext{years}} approx { ext{5 years}} cr} $$

[#2] What sum will amount to Rs. 7000 in 5 years at $${ ext{3}}frac{1}{3}$$ % simple interest ?
Correct Answer

(C) Rs. 6000

Explanation

Solution: $$eqalign{
& { ext{Amount Rs 7000}} cr
& { ext{Total interest in 5 years}} cr
& { ext{ = 5}} imes frac{{10}}{3}\% = frac{{50}}{3}\% = frac{1}{6} cr} $$ Principal Amount 6 (6 + 1) ↓ × 1000 ↓ × 1000 6000 7000 Hence required principal
= Rs. 6000

[#3] Mohan lent some amount of money at 9% simple interest and an equal amount of money at 10% simple interest each for two years. If his total interest was Rs. 760, what amount was lent in each case ?
Correct Answer

(D) Rs. 2000

Explanation

Solution: Let the amount invested = Rs. P According to the questions, $$eqalign{
& Leftrightarrow frac{{{ ext{P}} imes 9 imes { ext{2}}}}{{100}} + frac{{{ ext{P}} imes { ext{10}} imes { ext{2}}}}{{100}} = 760 cr
& Leftrightarrow frac{{ {18{ ext{P + 20P}}} }}{{100}} = 760 cr
& Leftrightarrow 38{ ext{P = 76000}} cr
& Leftrightarrow { ext{P = 2000}} cr} $$ Alternate Total interest percent $$eqalign{
& { ext{ = }}left( {9 imes 2}
ight)\% + left( {10 imes 2}
ight)\% cr
& Rightarrow 38\% = 760 cr
& Rightarrow 100\% = 2000 cr} $$ Hence required principal = Rs. 2000

[#4] If the simple interest on a sum of money for 15 months at $${ ext{7}}frac{1}{2}$$ % per annum exceeds the simple interest on the same sum for 8 months at $${ ext{12}}frac{1}{2}$$ % per annum by Rs. 32.50, then the sum of money ( In Rs.) is ?
Correct Answer

(C) Rs. 3120

Explanation

Solution: $$eqalign{
& {{ ext{T}}_1} = 15operatorname{months} cr
& ,,,,,, = frac{{15}}{{12}}years cr
& {R_1} = 7frac{1}{2}\% = frac{{15}}{2}\% cr
& {{ ext{T}}_2} = 8operatorname{months} cr
& ,,,,,,, = frac{8}{{12}}years cr
& {{ ext{R}}_2} = 12frac{1}{2}\% = frac{{25}}{2}\% cr
& { ext{Let the principal}} = { ext{P}} cr
& { ext{According to the question,}} cr
& Leftrightarrow frac{{{ ext{P}} imes { ext{15}} imes { ext{15}}}}{{12 imes 2 imes 100}} - frac{{{ ext{P}} imes 25 imes 8}}{{12 imes 2 imes 100}} = 32.50 cr
& Rightarrow frac{{225{ ext{P}}}}{{2400}} - frac{{200{ ext{P}}}}{{2400}} = 32.50 cr
& Rightarrow frac{{25{ ext{P}}}}{{2400}} = 32.50 cr
& Rightarrow { ext{P = Rs 3120}} cr
& { ext{Hence required principal}} cr
& { ext{ = Rs}}{ ext{. 3120}} cr} $$

[#5] Deepak invested an amount of Rs. 21250 for 6 years. At what rate of simple interest will be obtain the total amount of Rs. 26350 at the end of 6 years?
Correct Answer

5 p.c.p.a

Explanation

Solution: $$eqalign{
& { ext{P}} = { ext{Rs}}{ ext{.}},{ ext{21250}} cr
& { ext{S}}{ ext{.I}}{ ext{.}} = { ext{Rs}}{ ext{.}},left( {{ ext{26350}} - { ext{21250}}}
ight) cr
& ,,,,,,,,,, = { ext{Rs}}{ ext{.}},5100 cr
& { ext{T}} = { ext{6 years}} cr
& herefore { ext{Rate}} = left( {frac{{100 imes 5100}}{{{ ext{21250}} imes { ext{6}}}}}
ight)\% cr
& ,,,,,,,,,,,,,,,,,,, = 4\% cr} $$