Interest - Study Mode
[#181] A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:
Correct Answer
(D) 10%
Explanation
Solution: $$eqalign{
& { ext{Let}},{ ext{the}},{ ext{rate}},{ ext{be}},R\% ,{ ext{p}}{ ext{.a}}{ ext{.}},{ ext{Then,}} cr
& {frac{{5000 imes R imes 2}}{{100}}} + {frac{{3000 imes R imes 4}}{{100}}} cr
& = 2200. cr
& Rightarrow 100R + 120R = 2200 cr
& Rightarrow R = {frac{{2200}}{{220}}} = 10 cr
& herefore { ext{Rate}} = 10\% cr} $$
[#182] A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:
Correct Answer
(C) Rs. 15,000
Explanation
Solution: $$eqalign{
& { ext{Principal}} = Rs.,left( {frac{{100 imes 5400}}{{12 imes 3}}}
ight) cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,, = Rs.,15000 cr} $$
[#183] A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:
Correct Answer
(C) 12%
Explanation
Solution: $$eqalign{
& { ext{S}}{ ext{.I}}{ ext{. }}{kern 1pt} { ext{for 3 years}} cr
& = { ext{Rs}}{ ext{.}}left( {12005 - 9800}
ight) cr
& = { ext{Rs}}{ ext{. }}2205 cr
& { ext{S}}{ ext{.I}}{ ext{. for 5 years}} cr
& = { ext{Rs}}{ ext{.}},left( {frac{{2205}}{3} imes 5}
ight) cr
& = { ext{Rs}}{ ext{.}},3675 cr
& herefore { ext{Principal}} cr
& = { ext{Rs}}{ ext{.}},(9800 - 3675) cr
& = { ext{Rs}}{ ext{.}},6125 cr
& { ext{Hence,}},{ ext{rate}} = left( {frac{{100 imes 3675}}{{6125 imes 5}}}
ight)\% cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, = 12\% cr} $$
[#184] What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?
Correct Answer
(C) 2 : 3
Explanation
Solution: Let the principal be P and rate of interest be R%. Therefore Required ratio $$eqalign{
& = frac{{ {frac{{P imes R imes 6}}{{100}}} }}{{ {frac{{P imes R imes 9}}{{100}}} }} cr
& = frac{{6PR}}{{6PR}} cr
& = frac{6}{9} cr
& = 2:3 cr} $$
[#185] A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?
Correct Answer
(D) Cannot be determined
Explanation
Solution: We need to know the S.I., principal and time to find the rate. Since the principal is not given, so data is inadequate.