Interest - Study Mode
[#211] A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?
Correct Answer
3.6%
Explanation
Solution: Let the original rate be R%. Then, new rate = (2R)%. Note: Here, original rate is for 1 year(s)
the new rate is for only 4 months i.e. $$frac{1}{3}$$ year(s). $$eqalign{
& herefore {frac{{725 imes R imes 1}}{{100}}} + {frac{{362.50 imes 2R imes 1}}{{100 imes 3}}} cr
& = 33.50 cr
& Rightarrow left( {2175 + 725}
ight)R = 33.50 imes 100 imes 3 cr
& Rightarrow left( {2175 + 725}
ight)R = 10050 cr
& Rightarrow left( {2900}
ight)R = 10050 cr
& Rightarrow R = frac{{10050}}{{2900}} = 3.46 cr
& herefore ext{Original rate} = 3.46\% cr} $$
[#212] A man invested $$frac{{ ext{1}}}{{ ext{3}}}$$ of his capital at 7%
$$frac{{ ext{1}}}{{ ext{4}}}$$ at 8% and the remainder at 10%. If his annual income is Rs. 561, the capital is -
Correct Answer
(C) Rs. 6600
Explanation
Solution: Let total capital be Rs. x Then, $$ Rightarrow left( {frac{x}{3} imes frac{7}{{100}} imes 1}
ight) + left( {frac{x}{4} imes frac{8}{{100}} imes 1}
ight) + $$ xa0 xa0 xa0 $$left( {frac{{5x}}{{12}} imes frac{{10}}{{100}} imes 1}
ight)$$ xa0xa0 $$ = 561$$ $$eqalign{
& Rightarrow frac{{7x}}{{300}} + frac{x}{{50}} + frac{x}{{24}} = 561 cr
& Rightarrow 51x = left( {561 imes 600}
ight) cr
& Rightarrow x = left( {frac{{561 imes 600}}{{51}}}
ight) cr
& ,,,,,,,,,,,,,, = 6600 cr} $$
[#213] Rahul purchased a Maruti van for Rs. 1, 96,000 and the rate of depreciation is $$14frac{2}{7}\% $$xa0 per annum. Find the value of the van after two years.
Correct Answer
(B) Rs.1,44,000
Explanation
Solution: $$eqalign{
& { ext{Value}},{ ext{of}},{ ext{maruti}},{ ext{Van}},, cr
& {V_0} = Rs.,196000 cr
& { ext{Rate}},{ ext{of}},{ ext{depreciation}},, cr
& r = 14 {frac{2}{7}} \% = frac{{100}}{7}\%
cr
& { ext{Time}},,t = 2,{ ext{years}} cr
& { ext{Let}},{V_1},{ ext{is}},{ ext{the}},{ ext{value}},{ ext{after}},{ ext{depreciation}}. cr
& {V_1} = {V_0} imes {left[ {1 - left( {frac{r}{{100}}}
ight)}
ight]^t} cr
& {V_1} = 196000 imes {left[ {1 - left( {frac{{left( {frac{{100}}{7}}
ight)}}{{100}}}
ight)}
ight]^2} cr
& {V_1} = 196000 imes {left( {1 - {frac{1}{7}}}
ight)^2} cr
& {V_1} = 196000 imes {left( {frac{7-1}{7}}
ight)^2} cr
& {V_1} = 196000 imes {left( {frac{6}{7}}
ight)^2} cr
& {V_1} = frac{{left( {196000 imes 36}
ight)}}{{49}} cr
& {V_1} = Rs.,144000 cr} $$
[#214] What is the rate of simple interest for the first 4 years if the sum of Rs. 360 becomes Rs. 540 in 9 years and the rate of interest for the last 5 years is 6%?
Correct Answer
(B) 5%
Explanation
Solution: $$eqalign{
& { ext{Interest}},{ ext{for}},{ ext{the}},{ ext{last}},{ ext{5}},{ ext{years}} cr
& = frac{{PTR}}{{100}} cr
& = frac{{360 imes 5 imes 6}}{{100}} = Rs.,108 cr
& { ext{Interest}},{ ext{for}},{ ext{year}} = 540 - 360 = 180 cr
& { ext{So,}},{ ext{interest}},{ ext{for}},{ ext{first}},{ ext{four}},{ ext{years}} cr
& = 180 - 108 = Rs.,72
cr
& { ext{Now,}},{ ext{rate}},{ ext{for}},{ ext{first}},{ ext{four}},{ ext{years}} cr
& = frac{{ {72 imes 100} }}{{360 imes 4}} cr
& = 5\% cr} $$
[#215] Asif borrows Rs. 1500 from two moneylenders. He pays interest at the rate of 12% per annum for one loan and at the rate of 14% per annum for the other. The total interest he pays for the entire year is Rs. 186. How much does he borrow at the rate of 12%
Correct Answer
(A) Rs. 1200
Explanation
Solution: Let Asif lent Rs. X at 14% per year. Hence, Money lent at 12% = (1500 - x)
Given, total interest = Rs. 186 $$ {frac{{left( {x imes 14 imes 1}
ight)}}{{100}}} , + $$ xa0 xa0$$ {frac{{left[ {left( {1500 - x}
ight) imes 12 imes 1}
ight]}}{{100}}} $$ xa0 xa0xa0 = 186 $$eqalign{
& frac{{14x}}{{100}} + frac{{ {18000 - 12x} }}{{100}} = 186 cr
& 14x + 18000 - 12x = 186 imes 100 cr
& 2x = 18600 - 18000 cr
& x = frac{{600}}{2} = { ext{Rs}}{ ext{. }}300 cr
& { ext{Hence, money lent}}{kern 1pt} { ext{at }}12\% cr
& = 1500 - 300 cr
& = { ext{Rs}}{ ext{.}},1200 cr} $$