Interest - Study Mode

[#31] In a certain time, a sum becomes 4 times of itself on simple interest at the rate of 10% per annum. What is the rate of interest if the same sum becomes 7 times of itself in the same duration?
Correct Answer

(D) 20%

[#32] Rs. 2,500, when invested for 8 years at a given rate of simple interest per year, amounted to Rs. 3,725 on maturity. What was the rate of simple interest that was paid per annum?
Correct Answer

(B) 6.125%

Explanation

Solution: $$eqalign{
& { ext{Simple interest}} = 3725 - 2500 = 1225 cr
& { ext{SI}} = frac{{P imes r imes t}}{{100}} cr
& 1225 = frac{{2500 imes r imes 8}}{{100}} cr
& r = frac{{49}}{8} cr
& r = 6.125\% cr} $$

[#33] In how many least number of complete years a sum of money become more than four times of itself at the rate of 50% per annum on simple interest?
Correct Answer

(C) 6 years

Explanation

Solution: $$eqalign{
& { ext{SI}} = frac{{{ ext{PRT}}}}{{100}} cr
& 3x = frac{{x imes 50 imes { ext{T}}}}{{1.0}} cr
& { ext{T}} = frac{{3 imes 100}}{{50}} cr
& { ext{T}} = 6 cr} $$ In T = 6 yrs it will become 4 times For making it more than 4 time check what the time least time after 6 years in option.

[#34] A sum of Rs. 8,400 amounts to Rs. 11,046 at 8.75% p.a. simple interest in a certain time. What will be the simple interest (in Rs.) on a sum of Rs. 10,800 at the same rate for the same time?
Correct Answer

(C) 3,402

Explanation

Solution: $$eqalign{
& { ext{A}} = { ext{P}} + { ext{S}}{ ext{.I}}{ ext{.}} cr
& { ext{S}}{ ext{.I}}{ ext{.}} = frac{{{ ext{P}} imes { ext{R}} imes { ext{T}}}}{{100}} cr
& 11046 = 8400 + frac{{8400 imes 8.75 imes { ext{T}}}}{{100}} cr
& 2646 = frac{{84 imes 875 imes { ext{T}}}}{{100}} cr
& 2646 = 21 imes 35 imes { ext{T}} cr
& { ext{T}} = 3.6{ ext{ years}} cr
& { ext{S}}{ ext{.I}}{ ext{.}} = frac{{10800 imes 8.75 imes 3.6}}{{100}} cr
& = frac{{108 imes 875 imes 36}}{{1000}} cr
& = 3402 cr} $$

[#35] The simple interest on Rs. 7,300 at 15% p.a. from 28 th April to 4 th November, approximately is
Correct Answer

(A) Rs. 570.00

Explanation

Solution: $$eqalign{
& P = 7300 cr
& R = 15\% { ext{ per annum}} cr
& = frac{{15}}{{365}}{ ext{ per day}} cr
& t = { ext{2}}{{ ext{8}}^{{ ext{th}}}}{ ext{ April to }}{{ ext{4}}^{{ ext{th}}}}{ ext{ November}} cr
& t = 190{ ext{ days}} cr
& { ext{SI}} = frac{{PRT}}{{100}} cr
& = frac{{7300}}{{100}} imes frac{{15}}{{365}} imes 190 cr
& = 570{ ext{ Answer}} cr} $$