Interest - Study Mode

[#196] In how many years will a sum of money double itself at 18.75% per annum simple interest?
Correct Answer

(B) 5 years 4 months

Explanation

Solution: $$eqalign{
& { ext{Let sum = Rs}}{ ext{. }}x{ ext{}} cr
& { ext{Then,}} cr
& { ext{S}}{ ext{.I}}{ ext{. = Rs}}{ ext{. }}x{ ext{}} cr
& herefore ext{Time} = left( {frac{{100 imes { ext{S}}{ ext{.I}}{ ext{.}}}}{{{ ext{P}} imes { ext{R}}}}}
ight) cr
& = left( {frac{{100 imes x}}{{x imes 18.75}}}
ight){ ext{years}} cr
& = frac{{26}}{3}{ ext{years}} cr
& = 5frac{1}{3}{ ext{years}} cr
& = { ext{5 years 4 months}}{ ext{}} cr} $$

[#197] In how many years will the simple interest on a sum of money be equal to the principal at the rate of $$16frac{2}{3}$$ % per annum ?
Correct Answer

(C) 6 years

Explanation

Solution: $$eqalign{
& { ext{16}}frac{2}{3} = frac{{1 o { ext{ Interest}}}}{{6 o { ext{ Principal }}}} cr
& { ext{Let principal = 6}} cr
& { ext{Interest = 6}} cr
& { ext{Time = t years}} cr
& { ext{By using formula }} cr
& { ext{6}} = frac{{6 imes 50 imes { ext{t}}}}{{3 imes 100}} cr
& Rightarrow { ext{t}} = 6,{ ext{years}} cr} $$ Alternate Note : In such type of questions to save your valuable time think like the given way. $$eqalign{
& { ext{Rate}}\% cr
& { ext{ = 16}}frac{2}{3}\% = frac{{1 o { ext{ Interest}}}}{{6 o { ext{ Principal }}}} cr
& { ext{Represent for 1 years}} cr
& { ext{According to the question,}} cr
& { ext{Principal = Interest}} cr
& { ext{6 = 1}} imes { ext{6}} cr
& { ext{Hence,}} cr
& { ext{Time = 1}} imes { ext{6}} cr
& ,,,,,,,,,,,,{ ext{ = 6 years}} cr} $$ Note : If interest will be six times then time will also be six times.

[#198] A sum of money was invested at a certain rate of simple interest for 2 years. Had it been invested at 1% higher rate, it would have fetched Rs. 24 more interest. The sum of money is ?
Correct Answer

(A) Rs. 1200

Explanation

Solution: More interest paid in 2 years $$eqalign{
& { ext{ = 2}} imes { ext{1}} = { ext{2}}\% cr
& { ext{According to the question, }} cr
& { ext{2}}\% { ext{ of sum = Rs}}{ ext{. 24}} cr
& { ext{1}}\% { ext{ of sum = Rs}}{ ext{.}}frac{{24}}{2} cr
& { ext{Total sum}} cr
& { ext{ = Rs}}{ ext{. }}frac{{24}}{2} imes 100 cr
& = { ext{Rs}}{ ext{. }}1200 cr} $$

[#199] A man invests half of his capital at the rate of 10% per annum, one - third at 9% and the rest at 12% per annum. The average rate of interest per annum, which he gets is = ?
Correct Answer

(B) 10%

Explanation

Solution: Let the total amount = Rs. 6 Total average rate of interest $$eqalign{
& { ext{ = }}frac{{left( {3 imes 10\% }
ight) + left( {2 imes 9\% }
ight) + left( {1 imes 12\% }
ight)}}{6} cr
& = frac{{left( {30 + 18 + 12}
ight)}}{6} \% cr
& = 10\% cr} $$

[#200] A sum of money at simple interest doubles in 7 years. It will become four times in:
Correct Answer

(B) 21 years

Explanation

Solution: $$eqalign{
& { ext{Let sum}} = { ext{Rs}}{ ext{. }}x cr
& { ext{Then,}} cr
& { ext{S}}{ ext{.I}}{ ext{.}} = { ext{Rs}}{ ext{.}},x cr
& herefore ext{Rate},\% cr
& = left( {frac{{100 imes x}}{{x imes 7}}}
ight)\% cr
& = frac{{100}}{7}\% cr
& { ext{Now, sum}} = { ext{Rs}}{ ext{. }}x cr
& { ext{S}}{ ext{.I}}. = { ext{Rs}}{ ext{. }}3x cr
& ext{Rate} = frac{{100}}{7}\% cr
& herefore { ext{Total Time}} cr
& = left( {frac{{100 imes 3x}}{{x imes frac{{100}}{7}}}}
ight){ ext{years}} cr
& = 21,{ ext{years}} cr} $$