Interest - Study Mode

[#166] In how much time will the simple interest on a certain sum of money be $$frac{6}{5}$$ times of the sum of 20% per annum?
Correct Answer

(D) 6 years

Explanation

Solution: $$eqalign{
& 6 = 5 imes frac{{20}}{{100}} imes t cr
& t = 6{ ext{ years}} cr} $$

[#167] A sum of Rs. 10 is lent by a child to his friend to be returned in 11 monthly instalment a of Rs. 1 each, the interest being simple. The rate of interest is:
Correct Answer

(B) $$21frac{9}{{11}}\% $$

Explanation

Solution: Let the rate of interest be R% per annum = Amount to be paid. If paid at the end of 11 months $$ Rightarrow 10 + frac{{10 imes R imes frac{{11}}{{12}}}}{{100}} = 10 + frac{{11R}}{{120}}$$ Total effective payments = (Rs. 1 + Interest on Rs. 1 for 10 months) + (Rs. 1 + Interest on Rs. 1 for 9 months) + . . . . . + (Rs. 1 + Interest on Rs. 1 for 1 month) + Rs. 1 $$eqalign{
& = left( {1 + frac{{1 imes R imes frac{{10}}{{12}}}}{{100}}}
ight) + left( {1 + frac{{1 imes R imes frac{9}{{12}}}}{{100}}}
ight) + ..... + left( {1 + frac{{1 imes R imes frac{1}{{12}}}}{{100}}}
ight) + 1 cr
& = left( {1 + frac{{10R}}{{1200}}}
ight) + left( {1 + frac{{9R}}{{1200}}}
ight) + ..... + left( {1 + frac{R}{{1200}}}
ight) + 1 cr
& = 11 + frac{{Rleft( {frac{{10 imes 11}}{2}}
ight)}}{{1200}} cr
& = 11 + frac{{11R}}{{240}} cr
& { ext{Now we have}} cr
& 10 + frac{{11R}}{{120}} = 11 + frac{{11R}}{{240}} cr
& frac{{11R}}{{240}} = 1 cr
& R = frac{{240}}{{11}} cr
& x08oxed{R = 21frac{9}{{11}}\% } cr} $$

[#168] A sum of money at simple interest amounts of Rs. 6,000 in 4 years and to Rs. 6,750 in 7 years at the same rate percent p.a. of interest. The sum (in Rs.) is:
Correct Answer

(D) 5,000

Explanation

Solution: Simple interest for 3 years = 6750 - 6000 = 750 Simple interest for 1 year = 750 ÷ 3 = 250 Simple interest for 4 years = 4 × 250 = 1000 Sum = 6000 - 1000 = 5000

[#169] Sum Rs. 20000 and Rs. 40000 are given on simple interest at the rate of 10% and 15% per annum respectively for three years. What will be the total simple interest?
Correct Answer

(C) Rs. 24000

Explanation

Solution: Simple interest on 20000 for 3 years at 10% rate $${ ext{SI}} = frac{{20000 imes 3 imes 10}}{{100}} = 6000$$ Simple interest on 40000 for 3 years at 15% rate $${ ext{SI}} = frac{{40000 imes 3 imes 15}}{{100}} = 18000$$ Total interest = 6000 + 18000 = 24000

[#170] Find the simple interest on Rs. 2,700 for 8 months at 5 paisa per rupee per month?
Correct Answer

(D) Rs. 1,080

Explanation

Solution: $$eqalign{
& { ext{Rate}} = frac{{5{ ext{ paisa}}}}{{1{ ext{ rupee}}}} = 5\% cr
& { ext{Time}} = 8{ ext{ months}} cr
& { ext{S}}{ ext{.I}}{ ext{.}} = frac{{2700 imes 5 imes 8}}{{100}} = 1080 cr} $$