Interest - Study Mode
[#191] The simple interest on a sum of money is $$frac{1}{4}$$ of the principal and the number of years is equal to rate percent per annum. The rate percent is = ?
Correct Answer
(B) 5%
Explanation
Solution: $$eqalign{
& { ext{Principal}},,,,,{ ext{Interest}} cr
& underbrace {,,,,,,,4{ ext{P}},,,,,,,,,,,,,,,,,,,,{ ext{P}},,,,,,,,,,}_{} cr
& { ext{Time = Rate }}\% { ext{ (given)}} cr
& { ext{Now by using formula , }} cr
& { ext{P = }}frac{{4{ ext{P}} imes { ext{R}} imes { ext{R}}}}{{100}} cr
& Rightarrow {{ ext{R}}^2} = frac{{100}}{4} cr
& Rightarrow { ext{R = }}frac{{10}}{2} cr
& Rightarrow { ext{R = 5}}\% cr} $$
[#192] 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 as interest. The rate of interest per annum is = ?
Correct Answer
(D) 10%
Explanation
Solution: $$eqalign{
& { ext{Let the rate }}\% { ext{ = R}} cr
& { ext{According to the question,}} cr
& frac{{5000 imes 2 imes { ext{R}}}}{{100}} + frac{{3000 imes 4 imes { ext{R}}}}{{100}} = 2200 cr
& Rightarrow 100{ ext{R}} + 120{ ext{R}} = 2200 cr
& Rightarrow 220{ ext{R}} = 2200 cr
& Rightarrow { ext{R}} = 10\% cr
& { ext{Hence required rate}}\% cr
& = 10\% cr} $$
[#193] What annual installment will discharge a debt of Rs. 6450 due in 4 years at 5% simple interest = ?
Correct Answer
(A) Rs. 1500
Explanation
Solution: $$eqalign{
& { ext{By using formula,}} cr
& { ext{Installment}} cr
& { ext{ = }}frac{{6450 imes 100}}{{4 imes 100 + left( {3 + 2 + 1}
ight) imes 5}} cr
& { ext{ = }}frac{{6450 imes 100}}{{4 imes 100 + left( 6
ight) imes 5}} cr
& = frac{{6450 imes 100}}{{4 imes 100 + 30}} cr
& = frac{{6450 imes 100}}{{430}} cr
& = { ext{Rs}}{ ext{. 1500}} cr
& { ext{Hence value of installment}} cr
& { ext{ = Rs}}{ ext{. 1500}} cr} $$
[#194] A sum of money lent out at simple interest amounts to Rs. 720 after 2 years and to Rs.1020 after a further period of 5 years. The sum is
Correct Answer
(B) Rs. 600
Explanation
Solution: $$eqalign{
& { ext{S}}{ ext{.I}}{ ext{. for 5 years}} cr
& = { ext{Rs}}{ ext{.}}left( {1020 - 720}
ight) cr
& = { ext{Rs}}{ ext{. 300}} cr
& { ext{S}}{ ext{.I}}{ ext{. for 2 years}} cr
& = { ext{Rs}}{ ext{.}}left( {frac{{300}}{5} imes 2}
ight) cr
& = { ext{Rs}}{ ext{. }}120 cr
& herefore { ext{Principal}} cr
& = { ext{Rs}}{ ext{.}}left( {{ ext{720}} - 120}
ight) cr
& = { ext{Rs}}{ ext{. }}600 cr} $$
[#195] A sum of money becomes Rs. 20925 in 2 years and Rs. 24412.50 in 5 years. Find the rate of interest and the sum of money.
Correct Answer
(A) 6.25%, Rs. 18600
Explanation
Solution: $$eqalign{
& { ext{S}}{ ext{.I}}{ ext{. }}{ ext{for 3 years}} cr
& = { ext{Rs}}{ ext{.}}left( {24412.50 - 20925}
ight) cr
& = { ext{Rs}}{ ext{. }}3487.50 cr
& { ext{S}}{ ext{.I}}{ ext{. }}{ ext{for 2 years}} cr
& = { ext{Rs}}{ ext{.}}left( {frac{{3487.50}}{3} imes 2}
ight) cr
& = { ext{Rs}}{ ext{. }}2325 cr
& herefore ext{Principal} cr
& = { ext{Rs}}{ ext{.}}left( {20925 - 2325}
ight) cr
& = { ext{Rs}}{ ext{. }}18600 cr
& { ext{Hence,}} cr
& { ext{rate}} = left( {frac{{100 - 2325}}{{18600 imes 2}}}
ight)\% cr
& = 6.25\% cr} $$