1. 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) 3.6%

b) 4.5%

c) 5%

d) None of these

Explanation: Let the original rate be R%. Then, new rate = (2R)%.

Here, original rate is for 1 year(s); the new rate is for only 4 months i.e. $$\frac{1}{3}$$ year(s).

$$\eqalign{ & {\frac{{725 \times R \times 1}}{{100}}} + {\frac{{362.50 \times 2R \times 1}}{{100 \times 3}}} \cr & = 33.50 \cr & \Rightarrow \left( {2175 + 725} \right)R = 33.50 \times 100 \times 3 \cr & \Rightarrow \left( {2175 + 725} \right)R = 10050 \cr & \left( {2900} \right)R = 10050 \cr & R = \frac{{10050}}{{2900}} = 3.46 \cr & \text{Original rate} = 3.46\% \cr} $$

2. A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:

a) Rs. 2000

b) Rs. 10,000

c) Rs. 15,000

d) Rs. 20,000

Explanation:

$$\eqalign{ & {\text{Principal}} = Rs.\,\left( {\frac{{100 \times 5400}}{{12 \times 3}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,15000 \cr} $$

3. A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:

a) 5%

b) 8%

c) 12%

d) 15%

Explanation:

$$\eqalign{ & {\text{S}}{\text{.I}}{\text{. }}{\kern 1pt} {\text{for 3 years}} \cr & = {\text{Rs}}{\text{.}}\left( {12005 - 9800} \right) \cr & = {\text{Rs}}{\text{. }}2205 \cr & {\text{S}}{\text{.I}}{\text{. for 5 years}} \cr & = {\text{Rs}}{\text{.}}\,\left( {\frac{{2205}}{3} \times 5} \right) \cr & = {\text{Rs}}{\text{.}}\,3675 \cr & {\text{Principal}} = {\text{Rs}}{\text{.}}\,(9800 - 3675) \cr & = {\text{Rs}}{\text{.}}\,6125 \cr & {\text{Rate}} = \left( {\frac{{100 \times 3675}}{{6125 \times 5}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 12\% \cr} $$

4. What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?

a) 1 : 3

b) 1 : 4

c) 2 : 3

d) Data inadequate

Explanation: Let the principal be P and rate of interest be R%.

Required ratio

$$\eqalign{ & = \frac{{ {\frac{{P \times R \times 6}}{{100}}} }}{{ {\frac{{P \times R \times 9}}{{100}}} }} \cr & = \frac{{6PR}}{{9PR}} \cr & = \frac{6}{9} \cr & = 2:3 \cr} $$

5. A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?

a) Rs. 35

b) Rs. 245

c) Rs. 350

d) Cannot be determined

Explanation: We need to know the S.I., principal and time to find the rate.

Since the principal is not given, so data is inadequate.

6. How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

a) 3.5 years

b) 4 years

c) 4.5 year

d) 5 years

Explanation:

$$\eqalign{ & {\text{Time}} = \left( {\frac{{100 \times 81}}{{450 \times 4.5}}} \right){\text{years}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 4\,{\text{years}} \cr} $$

7. Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?

a) 3.6

b) 6

c) 18

d) Cannot be determined

Explanation:

$$\eqalign{ & {\text{Let}}\,{\text{rate}}\, = R\% \,{\text{and}} \cr & {\text{Time}}\,{\text{ = }}\,{\text{R}}\,{\text{years}}{\text{}} \cr & {\frac{{1200 \times R \times R}}{{100}}} = 432 \cr & 12{R^2} = 432 \cr & {R^2} = 36 \cr & R = 6 \cr} $$

8. A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?

a) 3%

b) 4%

c) 5%

d) 6%

Explanation:

$$\eqalign{ & {\text{S}}{\text{.I}}{\text{.}} = Rs.\,\left( {15500 - 12500} \right) \cr & \,\,\,\,\,\,\,\,\,\, = Rs.\,3000 \cr & {\text{Rate}} = \left( {\frac{{100 \times 3000}}{{12500 \times 4}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6\% \cr} $$

9. An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:

a) 10%

b) 10.25%

c) 10.5%

d) None of these

Explanation:

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{sum}}\,{\text{be}}\,{\text{Rs}}{\text{.}}\,{\text{100}}{\text{.}}\, \cr & {\text{S}}{\text{.I}}{\text{.}}\,{\text{for}}\,{\text{first}}\,{\text{6}}\,{\text{months}} \cr & = Rs.\,\left( {\frac{{100 \times 10 \times 1}}{{100 \times 2}}} \right) \cr & = Rs.\,5 \cr & {\text{S}}{\text{.I}}{\text{.}}\,{\text{for}}\,{\text{last}}\,{\text{6}}\,{\text{months}} \cr & = Rs.\,\left( {\frac{{105 \times 10 \times 1}}{{100 \times 2}}} \right) \cr & = Rs.\,5.25 \cr} $$

So, amount at the end of 1 year

= Rs. (100 + 5 + 5.25)

= Rs. 110.25

Effective rate = (110.25 - 100) = 10.25%

10. A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:

a) 5%

b) 7%

c) 9%

d) 10%

Explanation:

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{rate}}\,{\text{be}}\,R\% \,{\text{p}}{\text{.a}}{\text{.}}\, \cr & {\frac{{5000 \times R \times 2}}{{100}}} + {\frac{{3000 \times R \times 4}}{{100}}} \cr & = 2200 \cr & \Rightarrow 100R + 120R = 2200 \cr & \Rightarrow R = {\frac{{2200}}{{220}}} = 10 \cr & {\text{Rate}} = 10\% \cr} $$