Quantitative Aptitude > Interest
SIMPLE INTEREST MCQs
Total Questions : 234
| Page 14 of 24 pages
Answer: Option D. -> Rs. 2760
According to the question,
$${\text{A}} + \left( {\frac{{{\text{A}} \times {\text{5}} \times {\text{2}}}}{{{\text{100}}}}} \right) = $$ $${\text{B}} + \left( {\frac{{{\text{B}} \times {\text{5}} \times {\text{3}}}}{{{\text{100}}}}} \right) = $$ $${\text{C}} + \left( {\frac{{{\text{C}} \times {\text{5}} \times {\text{4}}}}{{{\text{100}}}}} \right)$$
110A = 115B = 120C
22A = 23B = 24X
Ratio of amount ( by using L.C.M. of 22, 23 and 24)
$$\eqalign{
& {\text{276 : 264 : 253}} \cr
& {\text{A's loan = }}\frac{{276}}{{793}} \times {\text{7930}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 2760}} \cr} $$
According to the question,
$${\text{A}} + \left( {\frac{{{\text{A}} \times {\text{5}} \times {\text{2}}}}{{{\text{100}}}}} \right) = $$ $${\text{B}} + \left( {\frac{{{\text{B}} \times {\text{5}} \times {\text{3}}}}{{{\text{100}}}}} \right) = $$ $${\text{C}} + \left( {\frac{{{\text{C}} \times {\text{5}} \times {\text{4}}}}{{{\text{100}}}}} \right)$$
110A = 115B = 120C
22A = 23B = 24X
Ratio of amount ( by using L.C.M. of 22, 23 and 24)
$$\eqalign{
& {\text{276 : 264 : 253}} \cr
& {\text{A's loan = }}\frac{{276}}{{793}} \times {\text{7930}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 2760}} \cr} $$
Answer: Option C. -> Rs. 7300
$$\eqalign{
& {\text{According to the question,}} \cr
& {\text{Interest = Rs}}{\text{. 1 per day}} \cr
& \therefore {\text{Interest in one year}} \cr
& {\text{ = 1}} \times {\text{365 = Rs}}{\text{. 365}} \cr
& \therefore {\text{S}}{\text{.I}}{\text{. = }}\frac{{{\text{P}} \times {\text{T}} \times {\text{R}}}}{{100}} \cr
& \Rightarrow 365 = \frac{{{\text{P}} \times 5 \times 1}}{{100}} \cr
& \Rightarrow {\text{P}} = \frac{{365 \times 100}}{5} \cr
& \Rightarrow {\text{P}} = {\text{Rs}}{\text{. 7300}} \cr} $$
$$\eqalign{
& {\text{According to the question,}} \cr
& {\text{Interest = Rs}}{\text{. 1 per day}} \cr
& \therefore {\text{Interest in one year}} \cr
& {\text{ = 1}} \times {\text{365 = Rs}}{\text{. 365}} \cr
& \therefore {\text{S}}{\text{.I}}{\text{. = }}\frac{{{\text{P}} \times {\text{T}} \times {\text{R}}}}{{100}} \cr
& \Rightarrow 365 = \frac{{{\text{P}} \times 5 \times 1}}{{100}} \cr
& \Rightarrow {\text{P}} = \frac{{365 \times 100}}{5} \cr
& \Rightarrow {\text{P}} = {\text{Rs}}{\text{. 7300}} \cr} $$
Answer: Option A. -> 4% p.a.
Let the rates of interest in the former and latter cases be R% and (R + 1) % p.a.
Then,
$$\eqalign{
& 5000 \times {\text{R}} \times 4 = 4000 \times \left( {{\text{R}} + 1} \right) \times 4 \cr
& \Rightarrow \frac{{{\text{R}} + 1}}{{\text{R}}} = \frac{{5000 \times 4}}{{4000 \times 4}} \cr
& \Rightarrow 1 + \frac{1}{{\text{R}}} = 1 + \frac{1}{4} \cr
& \Rightarrow {\text{R}} = 4 \cr
& {\text{Hence,}} \cr
& {\text{Required rate}} = 4\% \,{\text{p}}{\text{.a}}{\text{.}} \cr} $$
Let the rates of interest in the former and latter cases be R% and (R + 1) % p.a.
Then,
$$\eqalign{
& 5000 \times {\text{R}} \times 4 = 4000 \times \left( {{\text{R}} + 1} \right) \times 4 \cr
& \Rightarrow \frac{{{\text{R}} + 1}}{{\text{R}}} = \frac{{5000 \times 4}}{{4000 \times 4}} \cr
& \Rightarrow 1 + \frac{1}{{\text{R}}} = 1 + \frac{1}{4} \cr
& \Rightarrow {\text{R}} = 4 \cr
& {\text{Hence,}} \cr
& {\text{Required rate}} = 4\% \,{\text{p}}{\text{.a}}{\text{.}} \cr} $$
Answer: Option C. -> Rs. 3000
$$\eqalign{
& {\text{According to the question,}} \cr
& {\text{Amount = Rs}}{\text{. 3144}} \cr
& {\text{Rate = 8}}\% \cr
& {\text{Let, Principal = Rs}}{\text{. }}x \cr
& \therefore {\text{Time = }} \cr
& \frac{{30 + 29 + 31 + 30 + 31 + 30 + 31 + 7}}{{366}} \cr
& = \frac{{219}}{{366}} \cr
& \therefore {\text{SI = }}\frac{{{\text{P}} \times {\text{R}} \times {\text{T}}}}{{100}} \cr
& \Rightarrow 3144 - x = \frac{{x \times 8 \times 219}}{{100 \times 366}} \cr
& = {\text{Rs}}{\text{. 3000}} \cr
& \cr
& {\bf{Alternate}} \cr
& \Rightarrow {\text{P}} + \frac{{{\text{P}} \times 8 \times \frac{{219}}{{365}}}}{{100}} = 3144 \cr
& \Rightarrow {\text{P}} + \frac{{{\text{P}} \times 8 \times \frac{3}{5}}}{{100}} = 3144 \cr
& \Rightarrow 100{\text{P}} + \frac{{24{\text{P}}}}{5} = 314400 \cr
& \Rightarrow \frac{{524{\text{P}}}}{5} = 314400 \cr
& \Rightarrow {\text{P = }}\frac{{314400 \times 5}}{{524}} \cr
& \Rightarrow {\text{P}} = {\text{600}} \times {\text{5}} \cr
& \Rightarrow {\text{P = Rs}}{\text{.}} \, 3000 \cr} $$
$$\eqalign{
& {\text{According to the question,}} \cr
& {\text{Amount = Rs}}{\text{. 3144}} \cr
& {\text{Rate = 8}}\% \cr
& {\text{Let, Principal = Rs}}{\text{. }}x \cr
& \therefore {\text{Time = }} \cr
& \frac{{30 + 29 + 31 + 30 + 31 + 30 + 31 + 7}}{{366}} \cr
& = \frac{{219}}{{366}} \cr
& \therefore {\text{SI = }}\frac{{{\text{P}} \times {\text{R}} \times {\text{T}}}}{{100}} \cr
& \Rightarrow 3144 - x = \frac{{x \times 8 \times 219}}{{100 \times 366}} \cr
& = {\text{Rs}}{\text{. 3000}} \cr
& \cr
& {\bf{Alternate}} \cr
& \Rightarrow {\text{P}} + \frac{{{\text{P}} \times 8 \times \frac{{219}}{{365}}}}{{100}} = 3144 \cr
& \Rightarrow {\text{P}} + \frac{{{\text{P}} \times 8 \times \frac{3}{5}}}{{100}} = 3144 \cr
& \Rightarrow 100{\text{P}} + \frac{{24{\text{P}}}}{5} = 314400 \cr
& \Rightarrow \frac{{524{\text{P}}}}{5} = 314400 \cr
& \Rightarrow {\text{P = }}\frac{{314400 \times 5}}{{524}} \cr
& \Rightarrow {\text{P}} = {\text{600}} \times {\text{5}} \cr
& \Rightarrow {\text{P = Rs}}{\text{.}} \, 3000 \cr} $$
Answer: Option D. -> $$21\frac{9}{{11}}$$ %
⇒ 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
$$\eqalign{
& \therefore {\text{Rate}} = \left( {\frac{{100 \times 12}}{{1 \times 55}}} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 21\frac{9}{{11}}\% \cr} $$
⇒ 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
$$\eqalign{
& \therefore {\text{Rate}} = \left( {\frac{{100 \times 12}}{{1 \times 55}}} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 21\frac{9}{{11}}\% \cr} $$
Answer: Option A. -> Rs. 1368
Number of days
= 26 + 28 + 31 + 30 + 30 + 31
= 146 days
$$\eqalign{
& \Rightarrow {\text{SI = }}\frac{{{\text{P}} \times {\text{R}} \times {\text{T}}}}{{100}} \cr
& \Rightarrow {\text{SI = }}\frac{{36000 \times 9.5 \times 146}}{{100}} \cr
& \Rightarrow {\text{SI = Rs}}{\text{. 1368}} \cr} $$
Number of days
= 26 + 28 + 31 + 30 + 30 + 31
= 146 days
$$\eqalign{
& \Rightarrow {\text{SI = }}\frac{{{\text{P}} \times {\text{R}} \times {\text{T}}}}{{100}} \cr
& \Rightarrow {\text{SI = }}\frac{{36000 \times 9.5 \times 146}}{{100}} \cr
& \Rightarrow {\text{SI = Rs}}{\text{. 1368}} \cr} $$
Answer: Option D. -> Data inadequate
$$\eqalign{
& {\text{Let the sum be Rs}}{\text{. }}x \cr
& {\text{Rate be R}}\% {\text{ p}}{\text{.a}}{\text{.}} \cr
& {\text{Time be T years}}{\text{.}} \cr
& {\text{Then,}} \cr
& \left[ {\frac{{x \times \left( {{\text{R}} \times 2} \right) \times {\text{T}}}}{{100}}} \right] - \left( {\frac{{x \times {\text{R}} \times {\text{T}}}}{{100}}} \right) = 108 \cr
& \Leftrightarrow 2x{\text{T}} = 10800\,........(i) \cr
& And, \cr
& \left[ {\frac{{x \times {\text{R}} \times \left( {{\text{T}} + 2} \right)}}{{100}}} \right] - \left( {\frac{{x \times {\text{R}} \times {\text{T}}}}{{100}}} \right) = 108 \cr
& \Leftrightarrow 2x{\text{R}} = 18000\,.......(ii) \cr} $$
Clearly, from (i) and (ii), we cannot the find the value of x.
So, the data is inadequate.
$$\eqalign{
& {\text{Let the sum be Rs}}{\text{. }}x \cr
& {\text{Rate be R}}\% {\text{ p}}{\text{.a}}{\text{.}} \cr
& {\text{Time be T years}}{\text{.}} \cr
& {\text{Then,}} \cr
& \left[ {\frac{{x \times \left( {{\text{R}} \times 2} \right) \times {\text{T}}}}{{100}}} \right] - \left( {\frac{{x \times {\text{R}} \times {\text{T}}}}{{100}}} \right) = 108 \cr
& \Leftrightarrow 2x{\text{T}} = 10800\,........(i) \cr
& And, \cr
& \left[ {\frac{{x \times {\text{R}} \times \left( {{\text{T}} + 2} \right)}}{{100}}} \right] - \left( {\frac{{x \times {\text{R}} \times {\text{T}}}}{{100}}} \right) = 108 \cr
& \Leftrightarrow 2x{\text{R}} = 18000\,.......(ii) \cr} $$
Clearly, from (i) and (ii), we cannot the find the value of x.
So, the data is inadequate.
Question 138. 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 ?
Answer: Option B. -> Rs. 118000
$$\eqalign{
& {\text{Sum of the 12 years age }} \cr
& {\text{ = Rs}}{\text{. 100000}} \cr
& {\text{Sum of the 18 years age }} \cr
& = {\text{P}} + \frac{{{\text{P}} \times {\text{R}} \times {\text{T}}}}{{100}} \cr
& = {\text{100000}} + \frac{{100000 \times 6 \times 6}}{{100}} \cr
& = {\text{100000}} + {\text{36000}} \cr
& = {\text{136000}} \cr} $$
Total expenses
= 2500 + 500 = 3000 per year
Total expenses ( 6 years )
= 3000 × 6 = Rs. 18000
Amount obtained
= 136000 - 18000
= 118000
$$\eqalign{
& {\text{Sum of the 12 years age }} \cr
& {\text{ = Rs}}{\text{. 100000}} \cr
& {\text{Sum of the 18 years age }} \cr
& = {\text{P}} + \frac{{{\text{P}} \times {\text{R}} \times {\text{T}}}}{{100}} \cr
& = {\text{100000}} + \frac{{100000 \times 6 \times 6}}{{100}} \cr
& = {\text{100000}} + {\text{36000}} \cr
& = {\text{136000}} \cr} $$
Total expenses
= 2500 + 500 = 3000 per year
Total expenses ( 6 years )
= 3000 × 6 = Rs. 18000
Amount obtained
= 136000 - 18000
= 118000
Answer: Option D. -> 38.71 % p.a.
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
$$\eqalign{
& = {\text{Rs}}{\text{.}}\left( {22000 + 22000 \times \frac{5}{{12}} \times \frac{{\text{R}}}{{100}}} \right) \cr
& = {\text{Rs}}{\text{.}}\left( {22000 + \frac{{275{\text{R}}}}{3}} \right) \cr} $$
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
$$ = {\text{Rs}}{\text{.}}\left( {24000 + {\text{4800}} \times {\text{R}} \times \frac{{10}}{{12}} \times \frac{1}{{100}}} \right) = $$ $${\text{Rs}}{\text{.}}\left( {24000 + 40{\text{R}}} \right)$$
$$\eqalign{
& \therefore 22000 + \frac{{275{\text{R}}}}{3} = 24000 + 40{\text{R}} \cr
& \Rightarrow \frac{{155}}{3} = 2000 \cr
& \Rightarrow {\text{R}} = \frac{{2000 \times 3}}{{155}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 38.71\% \,{\text{p}}{\text{.a}}{\text{.}} \cr} $$
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
$$\eqalign{
& = {\text{Rs}}{\text{.}}\left( {22000 + 22000 \times \frac{5}{{12}} \times \frac{{\text{R}}}{{100}}} \right) \cr
& = {\text{Rs}}{\text{.}}\left( {22000 + \frac{{275{\text{R}}}}{3}} \right) \cr} $$
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
$$ = {\text{Rs}}{\text{.}}\left( {24000 + {\text{4800}} \times {\text{R}} \times \frac{{10}}{{12}} \times \frac{1}{{100}}} \right) = $$ $${\text{Rs}}{\text{.}}\left( {24000 + 40{\text{R}}} \right)$$
$$\eqalign{
& \therefore 22000 + \frac{{275{\text{R}}}}{3} = 24000 + 40{\text{R}} \cr
& \Rightarrow \frac{{155}}{3} = 2000 \cr
& \Rightarrow {\text{R}} = \frac{{2000 \times 3}}{{155}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 38.71\% \,{\text{p}}{\text{.a}}{\text{.}} \cr} $$
Answer: Option A. -> $$1\frac{1}{2}$$ times
Let Sum = Rs. x. Then, S.I. = Rs. x, Time = 16 years
$$\eqalign{
& \therefore {\text{Rate}} = \left( {\frac{{100 \times x}}{{x \times 16}}} \right)\% = {\frac{25}{4}}\% = {6\frac{1}{4}}\% \cr
& {\text{Now, sum}} = {\text{Rs}}{\text{. }}x, \cr
& {\text{Time}} = 8{\kern 1pt} {\text{years}} \cr
& {\text{Rate}} = 6\frac{1}{4}\% \cr
& \therefore {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {\frac{{x \times 25 \times 8}}{{100 \times 4}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}\frac{x}{2} \cr
& {\text{So,}} \cr
& {\text{Amount}} = {\text{Rs}}{\text{.}}\left( {x + \frac{x}{2}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}\frac{{3x}}{2} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1\frac{1}{2}{\text{ times}} \cr} $$
Let Sum = Rs. x. Then, S.I. = Rs. x, Time = 16 years
$$\eqalign{
& \therefore {\text{Rate}} = \left( {\frac{{100 \times x}}{{x \times 16}}} \right)\% = {\frac{25}{4}}\% = {6\frac{1}{4}}\% \cr
& {\text{Now, sum}} = {\text{Rs}}{\text{. }}x, \cr
& {\text{Time}} = 8{\kern 1pt} {\text{years}} \cr
& {\text{Rate}} = 6\frac{1}{4}\% \cr
& \therefore {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{.}}\left( {\frac{{x \times 25 \times 8}}{{100 \times 4}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}\frac{x}{2} \cr
& {\text{So,}} \cr
& {\text{Amount}} = {\text{Rs}}{\text{.}}\left( {x + \frac{x}{2}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}\frac{{3x}}{2} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1\frac{1}{2}{\text{ times}} \cr} $$
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