# Interest aptitude mcq

## Interest

 Question 1 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
Rs. 2100 is lent at compound interest of 5% per annum for 2 years. Find the amount after two years.
 A Rs. 2320 B Rs. 2315.25 C Rs. 2300 D Rs. 2310
Question 1 Explanation:
\begin{align} & {\text{We}}\,{\text{can}}\,{\text{use}}\,{\text{formula}}\,{\text{of}}\,{\text{compound}}\,{\text{interest}} \cr & A = P \times {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^n} \cr & A = 2100 \times {\left[ {1 + \left( {\frac{5}{{100}}} \right)} \right]^2} \cr & A = 2100 \times {\left[ {\frac{{105}}{{100}}} \right]^2} \cr & A = \frac{{\left( {2100 \times 11025} \right)}}{{10000}} \cr & {\text{Hence,}}\,{\text{Amount}}\,A = Rs.\,2315.25 \cr\end{align}

 Question 2 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
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:
 A Rs. 1800 B Rs. 5400 C Rs. 3600 D Data inadequate
Question 2 Explanation:
\begin{align} & {\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\end{align} Clearly, from (i) and (ii), we cannot the find the value of x.

 Question 3 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
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?
 A None of these B 5% C 3.60% D 4.50%
Question 3 Explanation:
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. 1/3 year(s).

\begin{align} & \therefore \left( {\frac{{725 \times R \times 1}}{{100}}} \right) + \left( {\frac{{362.50 \times 2R \times 1}}{{100 \times 3}}} \right) \cr & = 33.50 \cr & \Rightarrow \left( {2175 + 725} \right)R = 33.50 \times 100 \times 3 \cr & \Rightarrow \left( {2175 + 725} \right)R = 10050 \cr & \Rightarrow \left( {2900} \right)R = 10050 \cr & \Rightarrow R = \frac{{10050}}{{2900}} = 3.46 \cr & \therefore Original\,rate = 3.46\% \cr\end{align}

 Question 4 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
If the simple interest on Rs. 1 for 1 month is 1 paisa, then the rate percent per annum will be = ?
 A 12% B 10% C 8% D 6%
Question 4 Explanation:
\begin{align} & {\text{t}} = {\text{1 month = }}\frac{1}{{12}}{\text{year}} \cr & {\text{SI = 1 paisa = Rs}}{\text{. }}\frac{1}{{100}} \cr & {\text{r}}\% = \frac{{{\text{SI}} \times {\text{100}}}}{{{\text{P}} \times {\text{T}}}} = \frac{{1 \times 100 \times 12}}{{100 \times 1 \times 1}} \cr & {\text{r}}\% = 12\% \cr\end{align}
 Question 5 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
Rs. 1000 is invested at 5% per annum simple interest. If the interest is added to the principal after every years, the amount will become Rs. 2000 after = ?
 A 20 years B 15 years C 18 years D 162/3 years
Question 5 Explanation:
\begin{align} & {\text{Principal = Rs}}{\text{. 1000 }} \cr & {\text{Rate = 5}}\% \cr & {\text{Interest for first 10 years}} \cr & = \frac{{1000 \times 5 \times 10}}{{100}} \cr & = {\text{Rs}}{\text{. 500}} \cr & {\text{After 10 years principal}} \cr & = {\text{(1000}} + {\text{500)}} \cr & {\text{ = Rs}}{\text{. 1500}} \cr & {\text{Remaining interest}} \cr & {\text{ = Rs}}{\text{. (2000}} - {\text{1500)}} \cr & {\text{ = Rs}}{\text{. 500}} \cr & {\text{Required time }} \cr & {\text{ = }}\frac{{500}}{{1500}} \times \frac{{100}}{5} \cr & \Rightarrow \frac{{100}}{5} = \frac{{20}}{3} \cr & \Rightarrow 6\frac{2}{3}{\text{years}} \cr & {\text{Total time}} \cr & = \left( {10 + 6\frac{2}{3}} \right){\text{years}} \cr & {\text{ = 16}}\frac{2}{3}{\text{years}} \cr\end{align}

 Question 6 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
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:
 A 10% B 11% C 91/11% D 219/11%
Question 6 Explanation:
⇒ 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 \begin{align} & \therefore {\text{Rate}} = \left( {\frac{{100 \times 12}}{{1 \times 55}}} \right)\% \cr & = 21\frac{9}{{11}}\% . \cr\end{align}

 Question 7 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
A person invested some account at the rate of 12% simple interest and a certain amount at rate of 10% simple interest. He received yearly interest of Rs. 130. But if he had interchanged the amounts invested,he would have received Rs. 4 more as interest. How much did he invest at 12% simple interest ?
 A Rs. 400 B Rs. 800 C Rs. 500 D Rs. 700
Question 7 Explanation:
Let the amount invested at 12% be Rs. x and that invested at 10% be Rs. y \begin{align} & Then, \cr & \to 12\% \,{\text{of }}x + 10\% \,{\text{of }}y = 130 \cr & \Rightarrow 12x + 10y = 13000 \cr & \Rightarrow 6x + 5y = 6500.....{\text{(i)}} \cr & {\text{And,}} \cr & \to 10\% \,{\text{of }}x + 12\% \,{\text{of }}y = 134 \cr & \Rightarrow 10x + 12y = 13400 \cr & \Rightarrow 5x + 6y = 6700.....{\text{(ii)}} \cr & {\text{Adding (i) and (ii), we get:}} \cr & 11\left( {x + y} \right) = 13200 \cr & \Rightarrow x + y = 1200.....({\text{iii}}) \cr & {\text{Substracting (i) from (ii),}} \cr & {\text{we get: }} - x + y = 200.....({\text{iv}}) \cr & {\text{Adding (iii) and (iv), }} \cr & {\text{we get}}:2y = 1400\,or\,y = 700. \cr & {\text{Hence,}} \cr & {\text{Amount invested at}} \cr & 12\% = \left( {1200 - 700} \right) \cr & = {\text{Rs}}{\text{. 500}}. \cr\end{align}

 Question 8 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
Consider the following statements

If a sum of money is lent at simple interest, then the

I - money gets doubled in 5 years if the rate of interest is 162/3 %

II - money gets doubled in 5 years if the rate of interest is 20%.

III - money becomes four times in 10 years if it gets doubled in 5 years.

 A II alone is correct B I and III are correct C II and III are correct D III alone is correct
Question 8 Explanation:
\begin{align} & {\text{Let sum be x}}{\text{.}} \cr & {\text{Then,}} \cr & {\text{S}}{\text{.I}}{\text{.}} = x \cr & {\text{I - Time}} \cr & = \frac{{100 \times x}}{{x \times \frac{{50}}{3}}} \cr & = 6\,{\text{years(false)}} \cr & {\text{II}} - {\text{Time}} \cr & = \frac{{100 \times x}}{{x \times 20}} \cr & = 5\,{\text{years(True)}} \cr & III\, - {\text{Suppose sum}} = x. \cr & {\text{Then, S}}{\text{.I}}{\text{. }} = x \cr & {\text{Time }} = {\text{5 }}{\text{years}}{\text{.}} \cr & {\text{Rate}} = \left( {\frac{{100 \times x}}{{x \times 5}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\, = 20\% . \cr & \therefore {\text{Time}} = \left( {\frac{{100 \times 3x}}{{x \times 20}}} \right){\text{years}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 15\,{\text{years}}(false) \cr & {\text{So, B alone is correct}}{\text{.}} \cr\end{align}
 Question 9 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?
 A Rs. 6400 B Rs. 7200 C Rs. 6500 D Rs. 7500
Question 9 Explanation:
Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 - x).

Then, \begin{align} & \left( {\frac{{x \times 14 \times 2}}{{100}}} \right) + \left( {\frac{{\left( {13900 - x} \right) \times 11 \times 2}}{{100}}} \right) \cr & = 3508 \cr\end{align} ⇒ 28x - 22x = 350800 - (13900 x 22)

⇒ 6x = 45000

⇒ x = 7500.

So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400.

 Question 10 ->Click on any option to know the correct answers (सही उत्तर जानने के लिए किसी भी Choice पर क्लिक करें)
A person borrows Rs. 5000 for 2 year at 4% p.a. simple interest. He immediately lends it to another person at 61/4 % p.a. for 2 years. Find his gain in the transaction per year.
 A Rs. 125 B Rs. 112.50 C Rs. 150 D Rs. 167.50
Question 10 Explanation:
\begin{align} & {\text{Gain in 2 years}} \cr & = \left[ {\left( {5000 \times \frac{{25}}{4} \times \frac{2}{{100}}} \right) - \left( {\frac{{5000 \times 4 \times 2}}{{100}}} \right)} \right] \cr & = {\text{Rs}}{\text{.}}\left( {625 - 400} \right) \cr & = {\text{Rs}}{\text{. }}225. \cr & \therefore {\text{Gain 1 year}} = {\text{Rs}}{\text{.}}\left( {\frac{{225}}{2}} \right) \cr & = {\text{Rs}}{\text{. }}112.50 \cr\end{align}
There are 10 questions to complete.