Interest - Study Mode

[#101] Ram deposited a certain sum of money in a company at 12% per annum simple interest for 4 years and deposited equal amounts in fixed deposit in a bank for 5 years at 15% per annum simple interest. If the difference in the interest from two sources is Rs. 1350 then the sum deposited in each case is = ?
Correct Answer

(D) Rs. 5000

Explanation

Solution: Difference between their rates he gained from both boys $$eqalign{
& Rightarrow (15 imes 5)\% - (12 imes 4)\% cr
& Rightarrow 75\% - 48\% cr
& Rightarrow 27\% = 1350{ ext{ }}({ ext{given)}} cr
& Rightarrow 100\% = { ext{Rs}}{ ext{. 5000}} cr} $$

[#102] A some of money lent out at simple interest amount to Rs. 720 after 2 years and Rs. 1020 after a further period of 5 years. Find the principal ?
Correct Answer

(B) Rs. 600

Explanation

Solution: According to the question, Principal + SI for 2 year = Rs. 720 ......(i) Principal + SI for 7 year = Rs. 1020 ......(ii) Subtracting equation (i) from (ii) ⇒ SI for 5 years = (1020 - 720) = Rs. 300 ⇒ SI for 1 years = Rs. 60 ⇒ SI for 2 years = 60 × 2 = Rs. 120 ⇒ Principal amount = (Amount after 2 years - 2 years SI) = (720 - 120) ⇒ Principal amount = Rs. 600

[#103] A person invested some account at the rate of 12% simple interest and a certain amount at rate of 10% simple interest. He received yearly interest of Rs. 130. But if he had interchanged the amounts invested,he would have received Rs. 4 more as interest. How much did he invest at 12% simple interest ?
Correct Answer

(B) Rs. 500

Explanation

Solution: Let the amount invested at 12% be Rs. x and that invested at 10% be Rs. y $$eqalign{
& ext{Then,} cr
& o 12\% ,{ ext{of }}x + 10\% ,{ ext{of }}y = 130 cr
& Rightarrow 12x + 10y = 13000 cr
& Rightarrow 6x + 5y = 6500......{ ext{(i)}} cr
& { ext{And,}} cr
& o 10\% ,{ ext{of }}x + 12\% ,{ ext{of }}y = 134 cr
& Rightarrow 10x + 12y = 13400 cr
& Rightarrow 5x + 6y = 6700......{ ext{(ii)}} cr
& { ext{Adding (i) and (ii), we get:}} cr
& 11left( {x + y}
ight) = 13200 cr
& Rightarrow x + y = 1200.......({ ext{iii}}) cr
& { ext{Subtracting (i) from (ii),}} cr
& { ext{we get: }} - x + y = 200.......({ ext{iv}}) cr
& { ext{Adding (iii) and (iv), }} cr
& { ext{we get}}:2y = 1400,or,y = 700 cr
& { ext{Hence,}} cr
& { ext{Amount invested at 12%}} cr
& = left( {1200 - 700}
ight) cr
& = { ext{Rs}}{ ext{. 500}} cr} $$

[#104] Two equal sums of money are lent at the same time at 8% and 7% per annum simple interest. The former is recovered 6 months earlier than the latter and the amount in each case is Rs. 2560. The sum and the time for which the sums of money are lent out are.
Correct Answer

(A) Rs. 2000, 3.5 years and 4 years

Explanation

Solution: $$eqalign{
& { ext{Let each sum}} = { ext{Rs}}{ ext{. }}x. cr
& { ext{Let the first sum be invested for}} cr
& left( {T - frac{1}{2}}
ight){ ext{years and}} cr
& { ext{the second sum for }}T{ ext{ years}}{ ext{.}} cr
& { ext{Then,}} cr
& x + frac{{x imes 8 imes left( {T - frac{1}{2}}
ight)}}{{100}} = 2560 cr
& Rightarrow 100x + 8xT - 4x = 256000 cr
& Rightarrow 96x + 8xT = 256000....(i) cr
& { ext{And,}} cr
& x + frac{{x imes 7 imes T}}{{100}} = 2560 cr
& Rightarrow 100x + 7xT = 256000....(ii) cr
& { ext{From(i) and (ii), we get:}} cr
& 96x + 8xT = 100x + 7xT cr
& Rightarrow 4x = xT cr
& Rightarrow T = 4 cr
& { ext{Putting }}T = { ext{4 in (i),we get:}} cr
& 96x + 32x = 256000 cr
& Rightarrow 128x = 256000 cr
& Rightarrow x = 2000 cr
& { ext{Hence,}} cr
& { ext{each sum}} = { ext{Rs}}{ ext{. 2000}} cr
& { ext{time periods}} = cr
& { ext{4 years and }}3frac{1}{2}{ ext{years}} cr} $$

[#105] A sum of Rs. 7930 is divided into 3 parts and given at loan at 5% simple interest to A, B and C for 2, 3 and 4 years respectively. If the amounts of all three are equal after their respective periods of loan, then the A received a loan of = ?
Correct Answer

(D) Rs. 2760

Explanation

Solution: According to the question, $${ ext{A}} + left( {frac{{{ ext{A}} imes { ext{5}} imes { ext{2}}}}{{{ ext{100}}}}}
ight) = $$ xa0 xa0 $${ ext{B}} + left( {frac{{{ ext{B}} imes { ext{5}} imes { ext{3}}}}{{{ ext{100}}}}}
ight) = $$ xa0 xa0 $${ ext{C}} + left( {frac{{{ ext{C}} imes { ext{5}} imes { ext{4}}}}{{{ ext{100}}}}}
ight)$$ 110A xa0 = xa0 115B xa0 = xa0 120C 22A xa0 = xa0 xa0 23B xa0 = xa0 24X Ratio of amount ( by using L.C.M. of 22, 23 and 24) $$eqalign{
& { ext{276 : 264 : 253}} cr
& { ext{A's loan = }}frac{{276}}{{793}} imes { ext{7930}} cr
& ,,,,,,,,,,,,,,,,,,{ ext{ = Rs}}{ ext{. 2760}} cr} $$