Interest - Study Mode

[#66] For 2 years, a sum was put at SI at a certain rate. If the rate was 3% higher, it would have fetched Rs. 300 more. What will be the sum ?
Correct Answer

(A) Rs. 5000

Explanation

Solution: $$eqalign{
& { ext{Let principal is P}} cr
& { ext{then,}} cr
& { ext{300 = }}frac{{{ ext{P}} imes 3 imes 2}}{{100}} cr
& { ext{P = 5000}} cr} $$

[#67] A money lender claims to lend money at the rate of 10% per annum simple interest. However, he takes the interest in advance when he lends a sum for one year. At what interest rate does he lend the money actually ?
Correct Answer

(D) $$11frac{1}{9}$$ %

Explanation

Solution: $$eqalign{
& { ext{Amount}} o { ext{10}} cr
& ,,,,, downarrow cr
& ,,,,,90 o frac{{10}}{{90}} imes 100 cr
& ,,,,,,,,,, = 11frac{1}{9}\% cr} $$

[#68] A sum of Rs. 1550 was lent partly at 5% and partly at 8% p.a. simple interest. The total interest received after 3 years was Rs. 300. The ratio of the money lent at 5% to that lent at 8% is:
Correct Answer

(C) 16 : 15

Explanation

Solution: Let the sum lent at 5% be Rs. x and that lent 8% be Rs. (1550 - x). Then, $$eqalign{
& left( {frac{{x imes 5 imes 3}}{{100}}}
ight) + left[ {frac{{left( {1550 - x}
ight) imes 8 imes 3}}{{100}}}
ight] = 300 cr
& Leftrightarrow 15x - 24x + left( {1550 imes 24}
ight) = 30000 cr
& Leftrightarrow 9x = 7200 cr
& Leftrightarrow x = 800. cr
& herefore { ext{Required ratio}} = 800:750 cr
& = 16:15 cr} $$

[#69] A sum of Rs. 1440 is lent out in three parts in such away that the interests on first part at 2% for 3 years, second part at 3% for 4 years and third part at 4% for 5 years are equal. Then the difference between the largest and the smallest sum is -
Correct Answer

(D) Rs. 560

Explanation

Solution: Let the parts be Rs. x, Rs. y and Rs. [1440 - (x + y)]. Then, $$eqalign{
& = frac{{x imes 2 imes 3}}{{100}} = frac{{y imes 3 imes 4}}{{100}} cr
& = frac{{left[ {1440 - left( {x + y}
ight)}
ight] imes 4 imes 5}}{{100}} cr
& herefore 6x = 12y,or,x = 2y. cr
& So,frac{{x imes 2 imes 3}}{{100}} = frac{{left[ {1440 - left( {x + y}
ight)}
ight] imes 4 imes 5}}{{100}} cr
& Leftrightarrow 12y = left( {1440 - 3y}
ight) imes 20 cr
& Rightarrow 72y = 28800 cr
& Rightarrow y = 400 cr
& { ext{First part}} = x = 2y = { ext{Rs}}{ ext{. }}800, cr
& { ext{Second part}} = { ext{Rs}}{ ext{. }}400 cr
& { ext{Third part}} cr
& = { ext{Rs}}.left[ {1440 - left( {800 + 400}
ight)}
ight] cr
& = { ext{Rs}}{ ext{. }}240. cr
& herefore { ext{Required difference}} cr
& { ext{ = Rs}}{ ext{.}}left( {800 - 240}
ight) cr
& = { ext{Rs}}.560 cr} $$

[#70] A borrows a sum of Rs. 90,000 for 4 years at 5% simple interest. He lends it to B at 7% for 4 years at simple interest. What is his gain (in Rs.)?
Correct Answer

(C) 7,200

Explanation

Solution: $$eqalign{
& { ext{A's,}},{ ext{Principal}} = { ext{Rs}}{ ext{. }}90,000 cr
& { ext{Rate}} = 5\% cr
& { ext{Time}} = 4{ ext{ years}} cr
& herefore { ext{S}}{ ext{.I}} = frac{{90,000 imes 5 imes 4}}{{100}} = { ext{Rs}}{ ext{. }}18,000 cr
& { ext{B's,}},{ ext{Principal}} = { ext{Rs}}{ ext{. }}90,000 cr
& { ext{Rate}} = 7\% cr
& { ext{Time}} = 4{ ext{ years}} cr
& herefore { ext{S}}{ ext{.I}} = frac{{90,000 imes 7 imes 4}}{{100}} = { ext{Rs}}{ ext{. }}25,200 cr
& herefore { ext{Profit of A}} cr
& = left( {25,200 - 18,000}
ight) = { ext{Rs}}{ ext{. }}7,200 cr} $$