Interest - Study Mode

[#106] The principal which gives Rs 1 interest per day at a rate of 5% simple interest per annum is = ?
Correct Answer

(C) Rs. 7300

Explanation

Solution: $$eqalign{
& { ext{According to the question,}} cr
& { ext{Interest = Rs}}{ ext{. 1 per day}} cr
& herefore { ext{Interest in one year}} cr
& { ext{ = 1}} imes { ext{365 = Rs}}{ ext{. 365}} cr
& herefore { ext{S}}{ ext{.I}}{ ext{. = }}frac{{{ ext{P}} imes { ext{T}} imes { ext{R}}}}{{100}} cr
& Rightarrow 365 = frac{{{ ext{P}} imes 5 imes 1}}{{100}} cr
& Rightarrow { ext{P}} = frac{{365 imes 100}}{5} cr
& Rightarrow { ext{P}} = { ext{Rs}}{ ext{. 7300}} cr} $$

[#107] Arvind deposited a sum of money with a bank on 1 st january, 2012 at 8% simple interest per annum. He received an amount 3144 on 7 th August, 2012. The money he deposited with the bank was = ?
Correct Answer

(C) Rs. 3000

Explanation

Solution: $$eqalign{
& { ext{According to the question,}} cr
& { ext{Amount = Rs}}{ ext{. 3144}} cr
& { ext{Rate = 8}}\% cr
& { ext{Let, Principal = Rs}}{ ext{. }}x cr
& herefore { ext{Time = }} cr
& frac{{30 + 29 + 31 + 30 + 31 + 30 + 31 + 7}}{{366}} cr
& = frac{{219}}{{366}} cr
& herefore { ext{SI = }}frac{{{ ext{P}} imes { ext{R}} imes { ext{T}}}}{{100}} cr
& Rightarrow 3144 - x = frac{{x imes 8 imes 219}}{{100 imes 366}} cr
& = { ext{Rs}}{ ext{. 3000}} cr
& cr
& {x08f{Alternate}} cr
& Rightarrow { ext{P}} + frac{{{ ext{P}} imes 8 imes frac{{219}}{{365}}}}{{100}} = 3144 cr
& Rightarrow { ext{P}} + frac{{{ ext{P}} imes 8 imes frac{3}{5}}}{{100}} = 3144 cr
& Rightarrow 100{ ext{P}} + frac{{24{ ext{P}}}}{5} = 314400 cr
& Rightarrow frac{{524{ ext{P}}}}{5} = 314400 cr
& Rightarrow { ext{P = }}frac{{314400 imes 5}}{{524}} cr
& Rightarrow { ext{P}} = { ext{600}} imes { ext{5}} cr
& Rightarrow { ext{P = Rs}}{ ext{.}} , 3000 cr} $$

[#108] A man invested Rs. 5000 at some rate of simple interest and Rs. 4000 at 1 percent higher rate of interest. If the interest in both the cases after 4 years is same, the rate of interest in the former case is
Correct Answer

(A) 4% p.a.

Explanation

Solution: Let the rates of interest in the former and latter cases be R% and (R + 1) % p.a. Then, $$eqalign{
& 5000 imes { ext{R}} imes 4 = 4000 imes left( {{ ext{R}} + 1}
ight) imes 4 cr
& Rightarrow frac{{{ ext{R}} + 1}}{{ ext{R}}} = frac{{5000 imes 4}}{{4000 imes 4}} cr
& Rightarrow 1 + frac{1}{{ ext{R}}} = 1 + frac{1}{4} cr
& Rightarrow { ext{R}} = 4 cr
& { ext{Hence,}} cr
& { ext{Required rate}} = 4\% ,{ ext{p}}{ ext{.a}}{ ext{.}} cr} $$

[#109] Simple interest on Rs. 500 for 4 years at 6.25% per annum is equal to the simple interest on Rs. 400 at 5% per annum for a certain period of time. The period of time is = ?
Correct Answer

(C) $$6frac{1}{4}$$ years

Explanation

Solution: $$eqalign{
& { ext{Let the required time = t years }} cr
& { ext{According to the question,}} cr
& Leftrightarrow frac{{500 imes 4 imes 6.25}}{{100}} = frac{{400 imes 5 imes { ext{t}}}}{{100}} cr
& Leftrightarrow 5 imes 4 imes 625 = 400 imes 5 imes { ext{t}} cr
& Leftrightarrow { ext{t = }}frac{{625}}{{100}} = frac{{25}}{4} cr
& Leftrightarrow { ext{t}} = 6frac{1}{4}{ ext{years}} cr} $$

[#110] With a given rate of simple interest, the ratio of principal and amount for a certain period of time is 4 : 5. After 3 years with the same rate of interest, the ratio of the principal and amount becomes 5 : 7. The rate of interest is = ?
Correct Answer

(C) 5%

Explanation

Solution: $$eqalign{
& frac{{{ ext{Principal}}}}{{{ ext{Amount}}}} = frac{{4 imes 5}}{{5 imes 5}} cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,, = frac{{20}}{{25}} cr
& { ext{After three year}} cr
& frac{{ ext{P}}}{{ ext{A}}} = frac{{5 imes 4}}{{7 imes 4}} cr
& ,,,,,,,, = frac{{20}}{{28}} cr
& { ext{In three year S}}{ ext{.I}}{ ext{.}} cr
& = 28x - 25x cr
& = 3x cr
& ext{So, the required interest will be} cr
& 3x = frac{{20x imes { ext{R}} imes 3}}{{100}} cr
& { ext{R}} = 5\% cr} $$