Interest - Study Mode
[#161] A digital note-pad is available for Rs. 25,000 cash or Rs. 2,500 down payment followed by 4 equal monthly instalments. If the rate of interest charged is 24% per annum simple interest, what is the monthly instalment (in ., rounded off to the nearest tens)?
Correct Answer
(D) Rs. 5,900
Explanation
Solution: $$eqalign{
& { ext{Cash amount}} = 25000 cr
& { ext{Down payment}} = 2500 cr
& { ext{Remaining amount}} = 22500 cr
& { ext{Rate}} = 24\% ,{ ext{p}}{ ext{.a}} cr
& { ext{12 month}} o 24\% cr
& o frac{{24}}{{12}} imes 100 = frac{1}{{50}} cr
& 4{ ext{ month}} o 8\% cr
& Rightarrow { ext{Total amount}} = 22500 imes frac{{108}}{{100}} cr
& = 24300 cr} $$ [x08egin{array}{*{20}{c}}
{50}& - &{50} \
{50}& - &{51} \
{50}& - &{52} \
{50}& - &{mathop {53}limits_{\_\_\_\_\_\_} } \
{}&{}&{206}
end{array}] $$eqalign{
& { ext{EMI}} = frac{{24300 imes 50}}{{206}} cr
& = 5898.05 cr
& = 5900 cr} $$
[#162] The simple interest on a certain sum for 3 years at 14% p.a. is 4,200 less than the simple interest on the same sum for 5 years at the same rate. Find the sum.
Correct Answer
(C) Rs. 15,000
Explanation
Solution: $$eqalign{
& { ext{3 years total rate}} = 14 imes 3 = 42\% cr
& { ext{5 years total rate}} = 14 imes 5 = 70\% cr
& { ext{Gap}} = 28\% o 4200 cr
& { ext{Sum}} = frac{{4200}}{{28}} imes 100 = { ext{Rs}}{ ext{. }}15,000 cr} $$
[#163] A sum of Rs. 5,000 divided into two parts such that the simple interest on the first part for $$4frac{1}{5}$$xa0years at $$6frac{2}{3}\% $$ xa0p.a. is double the simple interest on the second part for $$2frac{3}{4}$$xa0years at 4% p.a. The ratio of the second part to the first part is:
Correct Answer
(C) 14 : 11
Explanation
Solution: $$eqalign{
& { ext{S}}{ ext{.}}{{ ext{I}}_1} = 2 imes { ext{S}}{ ext{.}}{{ ext{I}}_2} cr
& frac{{x imes 20 imes 21}}{{100 imes 3 imes 5}} = 2 imes frac{{y imes 4 imes 11}}{{100 imes 4}} cr
& 28x = 22y cr
& x:y = 22:28 cr
& { ext{Ratio of second part of first part}} cr
& y:x = 28:22 = 14:11 cr} $$
[#164] What will be the simple interest on a sum of Rs. 12000 at the rate of 15% per annum of three years?
Correct Answer
(A) Rs. 5400
Explanation
Solution: $${ ext{S}}{ ext{.I}}{ ext{.}} = frac{{12000 imes 15 imes 3}}{{100}} = { ext{Rs}}{ ext{. }}5400$$
[#165] A sum amounts to Rs. 14,395.20 at 9.25% p.a. simple interest in 5.4 years. What will be the simple interest on the same sum at 8.6% p.a. in 4.5 years?
Correct Answer
(A) Rs. 3,715.20
Explanation
Solution: $$eqalign{
& frac{{P imes 5.4 imes 9.25}}{{100}} = left( {14395.20 - P}
ight) cr
& P = 9600 cr
& frac{{9600 imes 8.6 imes 4.5}}{{100}} = { ext{SI}} cr
& { ext{SI}} = 3715.20 cr} $$