Interest - Study Mode

[#26] A sum of Rs. 10 is lent to be returned in 11 monthly instalments of Rs. 1 each, interest being simple. The rate of interest is:
Correct Answer

(D) $$21frac{9}{{11}}$$ %

Explanation

Solution: ⇒ Rs. 10 + S.I. on Rs. 10 for 11 months = Rs. 11 + S.I. on Rs. 1 for (1 + 2 + 3 + 4 + ........... + 10) months ⇒ Rs. 10 + S.I. on Rs. 1 for 110 months = Rs. 11 + S.I. on Rs. 1 for 55 months S.I. on Rs. 1 for 55 months = Rs. 1 $$eqalign{
& herefore { ext{Rate}} = left( {frac{{100 imes 12}}{{1 imes 55}}}
ight)\% cr
& ,,,,,,,,,,,,,,,,,,, = 21frac{9}{{11}}\% cr} $$

[#27] A computer is available for Rs. 39000 cash or Rs. 17000 as cash down payment followed by five monthly instalments of Rs. 4800 each. What is the rate of interest under the instalment plan?
Correct Answer

(D) 38.71 % p.a.

Explanation

Solution: Total cost of the computer = Rs. 39000 Down payment = Rs. 17000 Balance = Rs. (39000 - 17000) = Rs. 22000. Let the rate of interest be R% p.a. Amount of Rs. 22000 for 5 months $$eqalign{
& = { ext{Rs}}{ ext{.}}left( {22000 + 22000 imes frac{5}{{12}} imes frac{{ ext{R}}}{{100}}}
ight) cr
& = { ext{Rs}}{ ext{.}}left( {22000 + frac{{275{ ext{R}}}}{3}}
ight) cr} $$ The customer pays the shopkeeper Rs. 4800 after 1 month, Rs. 4800 after 2 months, ...... and Rs. 4800 after 5 months. Thus, the shopkeeper keeps Rs. 4800 for 4 months, Rs. 4800 for 3 months, Rs. 4800 for 2 months, Rs. 4800 for 1 months and Rs. 4800 at the end. ∴ sum of the amounts of these installments = (Rs. 4800 + S.I. on Rs 4800 for 4 months) + (Rs. 4800 + S.I. on Rs. 4800 for 3 months) + ...... + (Rs. 4800 + S.I. on Rs. 4800 for 1 month) + Rs. 4800 = Rs. (4800 × 5) + S.I. on Rs. 4800 for (4 + 3 + 2 + 1) months = Rs. 24000 + S.I. on Rs. 4800 for 10 months $$ = { ext{Rs}}{ ext{.}}left( {24000 + { ext{4800}} imes { ext{R}} imes frac{{10}}{{12}} imes frac{1}{{100}}}
ight) = $$ xa0 xa0 xa0 xa0 xa0$${ ext{Rs}}{ ext{.}}left( {24000 + 40{ ext{R}}}
ight)$$ $$eqalign{
& herefore 22000 + frac{{275{ ext{R}}}}{3} = 24000 + 40{ ext{R}} cr
& Rightarrow frac{{155}}{3} = 2000 cr
& Rightarrow { ext{R}} = frac{{2000 imes 3}}{{155}} cr
& ,,,,,,,,,,,,,, = 38.71\% ,{ ext{p}}{ ext{.a}}{ ext{.}} cr} $$

[#28] If the rate increases by 2%, the simple interest received on a sum of money increases by Rs. 108. If the time period is increased by 2 years, the simple interest on the same sum increases by Rs. 180. The sum is:
Correct Answer

(D) Data inadequate

Explanation

Solution: $$eqalign{
& { ext{Let the sum be Rs}}{ ext{. }}x cr
& { ext{Rate be R}}\% { ext{ p}}{ ext{.a}}{ ext{.}} cr
& { ext{Time be T years}}{ ext{.}} cr
& { ext{Then,}} cr
& left[ {frac{{x imes left( {{ ext{R}} imes 2}
ight) imes { ext{T}}}}{{100}}}
ight] - left( {frac{{x imes { ext{R}} imes { ext{T}}}}{{100}}}
ight) = 108 cr
& Leftrightarrow 2x{ ext{T}} = 10800,........(i) cr
& And, cr
& left[ {frac{{x imes { ext{R}} imes left( {{ ext{T}} + 2}
ight)}}{{100}}}
ight] - left( {frac{{x imes { ext{R}} imes { ext{T}}}}{{100}}}
ight) = 108 cr
& Leftrightarrow 2x{ ext{R}} = 18000,.......(ii) cr} $$ Clearly, from (i) and (ii), we cannot the find the value of x. So, the data is inadequate.

[#29] A boy aged 12 years is left with Rs. 100000 which is under a trust. The trustees invest the money at 6% per annum and pay the minor boy a sum of Rs. 2500, for his pocket money at the end of each year. The expenses of trust come out to be Rs. 500 per annum. Find the amount that will be handed over to the minor boy after he attains the age of 18 years ?
Correct Answer

(B) Rs. 118000

Explanation

Solution: $$eqalign{
& { ext{Sum of the 12 years age }} cr
& { ext{ = Rs}}{ ext{. 100000}} cr
& { ext{Sum of the 18 years age }} cr
& = { ext{P}} + frac{{{ ext{P}} imes { ext{R}} imes { ext{T}}}}{{100}} cr
& = { ext{100000}} + frac{{100000 imes 6 imes 6}}{{100}} cr
& = { ext{100000}} + { ext{36000}} cr
& = { ext{136000}} cr} $$ Total expenses = 2500 + 500 = 3000 per year Total expenses ( 6 years ) = 3000 × 6 = Rs. 18000 Amount obtained = 136000 - 18000 = 118000

[#30] The simple interest on Rs. 36000 for the period from 5 th January to 31 st May, 2013 at 9.5% per annum is = ?
Correct Answer

(A) Rs. 1368

Explanation

Solution: Number of days = 26 + 28 + 31 + 30 + 30 + 31 = 146 days $$eqalign{
& Rightarrow { ext{SI = }}frac{{{ ext{P}} imes { ext{R}} imes { ext{T}}}}{{100}} cr
& Rightarrow { ext{SI = }}frac{{36000 imes 9.5 imes 146}}{{100}} cr
& Rightarrow { ext{SI = Rs}}{ ext{. 1368}} cr} $$