Interest - Study Mode
[#46] If x, y, z are three sum of money such that y is the simple interest on x and z is the simple interest on y for the same time and at the same rate of interest, then what is the relation between x, y, z we have = ?
Correct Answer
(D) y 2 = zx
Explanation
Solution: Let the time is 't' years and the rate of interest is R% According to the question, $$eqalign{
& {x08f{Case(I):}} cr
& y = frac{{x imes { ext{R}} imes { ext{t}}}}{{100}}.....(i) cr
& {x08f{Case(II):}} cr
& z = frac{{y imes { ext{R}} imes { ext{t}}}}{{100}}.....(ii) cr} $$ By dividing equation (i) by equation (ii) $$eqalign{
& frac{y}{z} = frac{{x imes { ext{R}} imes { ext{t}}}}{{y imes { ext{R}} imes { ext{t}}}} cr
& Rightarrow {y^2} = zx cr} $$
[#47] Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 8160, the money borrowed by him (in Rupees) was?
Correct Answer
(C) Rs. 8000
Explanation
Solution: Let the money borrowed by Nitin = Rs. P According to the question, $$eqalign{
& frac{{{ ext{P}} imes 6 imes 3}}{{100}} + frac{{{ ext{P}} imes 9 imes 5}}{{100}} + frac{{{ ext{P}} imes 13 imes 3}}{{100}} = { ext{Rs}}{ ext{. }}8160 cr
& Rightarrow frac{{{ ext{18P}}}}{{100}} + frac{{{ ext{45P}}}}{{100}} + frac{{{ ext{39P}}}}{{100}} = { ext{Rs}}{ ext{. 1860}} cr
& Rightarrow frac{{{ ext{102P}}}}{{100}} = { ext{Rs}}{ ext{. 8160}} cr
& Rightarrow { ext{P = Rs}}{ ext{.}}frac{{8160 imes 100}}{{102}} cr
& ,,,,,,,,,,,,{ ext{ = Rs}}{ ext{. 8000}} cr} $$ Alternate Note : In such type of questions to save your valuable time follow the given below method. Let principal = Rs. 100 Total Interest $$frac{{100 imes 6 imes 3}}{{100}} + frac{{100 imes 9 imes 5}}{{100}} + $$ xa0 xa0xa0 $$frac{{100 imes 13 imes 3}}{{100}}$$ $$eqalign{
& = 18 + 45 + 39 cr
& = 102{ ext{ units}} cr
& { ext{According to the question,}} cr
& { ext{102 units = Rs}}{ ext{. 8160}} cr
& { ext{1 unit = Rs}}{ ext{. }}frac{{8160}}{{102}} cr
& ,,,,,,,,,,,,,,,,{ ext{ = Rs}}{ ext{. 80}} cr
& { ext{100 units = Rs}}{ ext{. 8000}} cr
& { ext{Hence sum = Rs}}{ ext{. 8000}} cr} $$ Alternate Total rate of interest in 11 years $$eqalign{
& left( {6 imes 3}
ight)\% + left( {5 imes 9}
ight)\% + left( {3 imes 13}
ight)\% { ext{ }} cr
& Rightarrow 102\% = 8160 cr
& Rightarrow 100\% = 8000 cr
& herefore { ext{Sum = Rs}}{ ext{. 8000}} cr} $$
[#48] A sum of Rs. 800 amounts to Rs. 920 in 3 years at the simple interest rate. If the rate is increased by 3% p.a. What will be the sum amount to in the same period ?
Correct Answer
(A) Rs. 992
Explanation
Solution: $$eqalign{
& { ext{Increased interest in 3 years}} cr
& { ext{ = 3}} imes { ext{3}} cr
& { ext{ = 9% }} cr
& { ext{Hence increased amount}} cr
& { ext{ = }}frac{{800 imes 9}}{{100}} cr
& = { ext{Rs}}{ ext{. }}72 cr
& { ext{Total amount}} cr
& { ext{ = }}left( {920 + 72}
ight) cr
& = { ext{Rs}}{ ext{. }}992 cr} $$
[#49] Simple interest on a certain amount is $$frac{9}{{16}}$$ of the principal. If the numbers representing the rate of interest in percent and time in years be equal, then time, for which the principal is lent out, is -
Correct Answer
(D) $$7frac{1}{2}$$ years
Explanation
Solution: $$eqalign{
& { ext{Let}},{ ext{sum}} = x. cr
& { ext{Then,}} cr
& { ext{S}}{ ext{.I}}{ ext{.}} = frac{{ ext{9}}}{{{ ext{16}}}}x cr
& { ext{Let rate}} = { ext{R}}\% , ext{and} cr
& ext{time} = R, ext{years} cr
& herefore left( {frac{{x imes { ext{R}} imes { ext{R}}}}{{100}}}
ight) = frac{{9x}}{{16}} cr
& Rightarrow {{ ext{R}}^2} = frac{{900}}{{16}} cr
& { ext{R}} = frac{{30}}{4} = 7frac{1}{2} cr
& { ext{Hence,}} cr
& { ext{time}} = 7frac{1}{2} ext{years} cr} $$
[#50] A lends Rs. 2500 to B and a certain sum to C at the same time at 7% p.a. simple interest. If after 4 years, A altogether receives Rs. 1120 as interest from B and C, then the sum lent to C is :
Correct Answer
(B) Rs. 1500
Explanation
Solution: Let the sum lent to C be Rs. x. Then, $$eqalign{
& left( {frac{{2500 imes 7 imes 4}}{{100}}}
ight) + left( {frac{{x imes 7 imes 4}}{{100}}}
ight) = 1120 cr
& Rightarrow frac{{7x}}{{25}} = left( {1120 - 700}
ight) cr
& Rightarrow x = left( {frac{{420 imes 25}}{7}}
ight) cr
& ,,,,,,,,,,,, = 1500. cr} $$