**Answer –** Option C

**Explanation –**

Effectively he borrowed Rs. 800 and returned Rs. 1000 after one year. So he paid Rs. 200 as interest on Rs. 800

i.e, Rate of interest = \(\frac {200} {800} * 100\) = 25%

**2. Rajan borrowed Rs. 50000 from Rakesh at simple interest. After 3 years, Rakesh got Rs. 3000 more than what he had given to Rajan. What was the rate of interest per annum ? **

**Answer –** Option A

**Explanation –**

Rate = \((\frac {100 * 300} {5000 * 3} )\)% = 2%

**3. Rakesh took a loan for 7 years at the rate of 6 % p.a. S.I. If total interest paid was Rs. 2100, then principal was**

**Answer –** Option C

**Explanation –**

Principal = Rs\((\frac {2100 * 100} {7 * 6} )\) = Rs. 500

**4. How much should money lender lend at simple rate of interest of 15% in order to have Rs. 3234 at the end of \( 1 \frac {1} {2}\) years**

**Answer –** Option D

**Explanation –**

Let required money be x

Then \(( x + \frac {x * 15} {100} * \frac {3}{2}\) = 3234

\(\frac {49 x} {40}\) = 3234

i.e, x = \(\frac {3234 * 40} {49}\) = 2640

**5. An amount Rs. 8000 becomes Rs. 9200 in 3 years at simple interest. If rate of interest is increased by 3%, it would amount to**

**Answer –** Option A

**Explanation –**

. Principal = Rs. 8000, S.I. = Rs. 1200,

Time = 3 years.

i.e, Rate = \((\frac {100 * 1200} {8000 * 3}) %\) = 5%

New rate = 8%, Principal = Rs. 8000,

Time = 3 years.

S.I = Rs. \((\frac {8000 * 8 * 3} {100})\) = Rs. 1920

i.e, New amount = Rs. (8000 + 1920)

= Rs. 9920

**6. A sum of money deposited at compound interest doubles itself in 4 years. It will amount to sixten times at the same rate in**

**Answer –** Option B

**Explanation –**

Let sum = Rs. 100, Time = 4 years,

Amount due in 4 years = Rs. 200

i.e, \(100 ({1 + \frac {10} {100}}^{4})\)

\( ({1 + \frac {10} {100}}^{4})\) = 2 …..(i)

Let the amount becomes 16 times in n years

i.e, \(100 ({1 + \frac {10} {100}}^{n})\) = 1600 ……..(ii)

\( ({1 + \frac {10} {100}}^{n})\) = 16

From equation (i) and (ii)

\({2}^{\frac {1} {4}}\) = 16 = \( {2}^{4}\)

\(\frac {n} {4}\) = 4

n = 16

**7. For how many years should Rs. 1200 be invested at 10% p.a. in order to earn the same simple interest as is earned by investing Rs. 1800 at 12% p.a. for 5 years ?**

**Answer –** Option A

**Explanation –**

S.I. required = Rs \(\frac {1800 * 12 * 5} {100}\)

= Rs. 1080.

\(\frac {100 * 1080} {120 * 10}\) = 9 years

**8. A sum of money was lent at simple interest at 11% p.a. for 3\(\frac {1} {2}\) years and 4 \(\frac {1} {2}\) years respectively. If difference in interests for two periods was Rs.5500, then the sum is**

**Answer –** Option C

**Explanation –**

Let the sum Rs. x. Then

(x * 11 * \(\frac {9} {2}\) * \(\frac {1} {100} – x * 11 \frac {7} {2} * \frac {1} {100}\)) = 5500

\(\frac {22x} {200}\) = 5500

11x = 550000

x = 50000

**9. Rajan lent Rs. 1200 to Rakesh for 3 years at a certain rate of simple interest and Rs. 1000 to Mukesh for the same time at the same rate. If he gets Rs. 50 more from Rakesh than from Mukesh, then the rate percent is**

**Answer –** Option A

**Explanation –**

\(\frac {1200 * r * 3} {100}\) – \(\frac {1000 * r * 3} {100}\) = 50

6r = 5o

r = 8 \(\frac {1} {3}\)%

**10. The difference between interests received from Canara Bank and Punjab & Sind Bank on Rs. 500 for 2 years is Rs. 2.50. The difference between their rates is**

**Answer –** Option C

**Explanation –**

\(\frac {500 * {r}_{1} * 2} {100}\) – \(\frac {500 * {r}^{2} * 2} {100}\) = 2. 50

1000 (\({r}_{1} – {r}_{2}\)) = 250

(\({r}_{1} – {r}_{2}\))\(\frac {250} {1000}\)% = \(\frac{1}{4}\) = 0.25%

**11. If compound interest for two successive years is Rs. 110 and Rs. 121 respectively, then the rate of interest is**

**Answer –** Option A

**Explanation –**

In the first year, interest = Rs. 110

In the second year, interest = Rs. 121

Thus an additional intereset of Rs. 11 is earned in the second year. This additional interest is earned on the interest earned in first year i.e., on Rs. 110.

i.e, Rate of interest \(\frac {11 * 100} {110 * 1}\) = 10%

**12. A money lender finds that due to a fall in the rate of interest from 8% to 7 \(\frac {3} {4}\) %, his yearly income diminishes by Rs. 615. His capital is**

**Answer –** Option B

**Explanation –**

Let the capital be Rs. x. Then

\(\frac {x * 8 * 1} {100}\) – x \(\frac {31} {4}\) * \(\frac {1} {100}\) = 615

32x â€“ 31x = 61500 * 4

x = 246000

**13. Mr. Mittal finds that an increase in the rate of interest from 4 \(\frac {7} {8}\) % to 5 \(\frac {1} {8}\) % per annum increases his yearly income by Rs. 250. His investment is**

**Answer –** Option A

**Explanation –**

Let the investment be Rs. x. Then

\(x * \frac {41} {8} * \frac {1} {100} – x \frac {39} {8} * \frac {1} {100}\) = 250

2x = 20000

x = 100000

**14. In how many years will a sum of money double itself at 4% per annum ?**

**Answer –** Option D

**Explanation –**

Let the sum be x. Then

S.I. = x

i.e, Time = \( \frac {100 * S.I} {Sum * Rate}\) = \(x * \frac {100 * x} {x * 4}\)

= 25 years

**15. At a certain rate of simple interest, a certain sum doubles itself in 10 years. It will
triple itself in**

**Answer –** Option C

**Explanation –**

Let the sum be x. Then

S.I. = x

Time = 10 years.

i.e, Rate = \( \frac {100 * x} {x * 10}\)% = 10%

Now, sum = x, S.I. = 2x, Rate = 10%

i.e, Time = \(\frac {100 * 2x} {x * 10}\)years = 20 years

**Answer –** Option C

**Explanation –**

SI = \(\frac {4800 * 8.S * 2.2S} {100}\) = Rs. 918

**2. Simple Interest on Rs. 500 for 4 years at 6.25% per annum is equal to the Simple Interest on
Rs.400 at 5% per annum for a certain period of time. The period of time is**

**Answer –** Option C

**Explanation –**

500 * 4 * 6.25% = 400 * 5 * t

t = 6.25 years

**3. A sum becomes Rs. 2916 in 2 years at 8% per annum compound interest. The sum is**

**Answer –** Option B

**Explanation –**

Let the required sum be Rs. x.

x * \(\frac {108} {100}\) * \(\frac {108} {100}\) = 2916

x = Rs. 2500

**4. If `200 becomes `240 in 4 years, then the rate of simple interest per annum is**

**Answer –** Option D

**Explanation –**

Given that Rs. 200 becomes Rs. 240 in 4 years, thus it would have become Rs. 210 at the end of first year.

Hence, rate of simple interest = \(\frac {10} {200}\) * 100 = 5%

**5. A sum of money doubles itself in 5 years when the interest is compounded annually. The number of years when it will become eight times is**

**Answer –** Option C

**Explanation –**

The money gets doubled in 5 years which means it becomes twice of itself after every 5 years. Hence, it will be increased to 4 times in 10 years and 8 times in 15 years.

**6. The simple interest on rupees 200 for 3 years at 6% per annum in rupees is**

**Answer –** Option A

**Explanation –**

SI = \(\frac {200 * 30 * 6} {100}\) = Rs. 36

**7. A sum of money doubles itself in 4 years when the interests is compounded annually. The number of years when it will become eight times is**

**Answer –** Option C

**Explanation –**

If the money gets doubled in 4 years then it will become 5 times in 8 years and 8 times in 12 years.**8. The simple interest on rupees 800 for 7 years at 5% per annum is**

**Answer –** Option A

**Explanation –**

Simple interest = \(\frac {PTR} {100}\)

= 800 * \(\frac {5} {100} * \frac {5} {2}\)

**9. The compound interest on rupees 12000 for 1 year at 10% per annum compounded half
yearly is**

**Answer –** Option B

**Explanation –**

Compound interest for \(\frac {1} {2}\)year = \(\frac {PTR} {100}\)

= 12000 * \(\frac {10} {100} * \frac {1} {2}\) = 600

Compound interest for next \(\frac {1} {2}\)year = 600 + 600 * \(\frac {10} {100} * \frac {1} {2}\) = 630

i.e, Total CL = 600 + 630

= Rs. 1230

**10. The simple interest on rupees 800 for 3 years at 5% per annum in rupees is**

**Answer –** Option C

**Explanation –**

SI = \(\frac {PTR} {100}\)

SI = 800 * = \(\frac {5} {100} * 3\) = 120

**11. Compound interest on rupees 8000 for 1 year at 10% per annum compounded half yearly is**

**Answer –** Option D

**Explanation –**

8000 * \(\frac {209} {200} * \frac {209} {200}\) = 8736.20

So, interest = 8736.20 âˆ’ 8000 = 736.20

**12. In how many years rupees 500 will amount to rupees 800 at simple interest of 10% per year **

**Answer –** Option A

**Explanation –**

Simple interest = Amount â€“ Principle

= 800 â€“ 500 = 300

SI = = \(\frac {PTR} {100}\) = 300

500 * = \(\frac {10} {100}\) * T

T = 6 years

**13. Compound interest Rs. 16000 for 1 year at 10% per annum compounded half yearly is**

**Answer –** Option B

**Explanation –**

Compound interest for \(\frac {1} {2}\)year = \(\frac {PTR} {100}\)

= 16000 * \(\frac {1} {10} * \frac {1} {2}\) = 800

Compound interest for 2nd \(\frac {1} {2}\)year

= 800 + 800 * \(\frac {1} {10} * \frac {1} {2}\) = 840

i.e, Total I = 800 + 840 = 1640

**14. In how many years `500 will amount to `700 at simple interest of 5% per annum?**

**Answer –** Option D

**Explanation –**

P = Rs. 500

A = Rs. 700

Interest = 200 = \(\frac {500 * 5 * T} {100}\)

T = 8 years

**15. In how many years Rs. 2000 will amount to Rs. 2100 at 10% per annum compounded half yearly**

**Answer –** Option D

**Explanation –**

A = \(({1 + \frac {r} {100}})^{T}\)

2100 = 2000 \(({1 + \frac {\frac {10}{2}} {100}})^{T}\)

1.05 = \(({1 + \frac {5} {100}})^{T}\)

No. of years = 0.5

**Answer –** Option A

**Explanation –**

A = 7500 * \({(1 +\frac {4} {100})}^{2}\) = 812

i.e, CI = 8112 â€“ 7500 = 612

**2. In how many years, a sum will be thrice of it at simple interest @10% per annum ?**

**Answer –** Option B

**Explanation –**

According to the question sum becomes thrice.

If Rs. P is invested, it becomes 3P

i.e, Interest earned = 2P

2P = \(\frac {P * 10 * T} {100}\)

T = 20years

**3. A sum of money amounts to Rs. 9680 in 2 years and Rs. 10648 in 3 years. The rate of interest per annum on compounded basis is**

**Answer –** Option B

**Explanation –**

According to the question

9680 = P \(({1 + \frac {r} {100}})^{2}\)

10648 = P \(({1 + \frac {r} {100}})^{3}\) = P \(\frac {10648} {9680}\) = P \(1 + \frac {r} {100}\)

1.1 = 1 + \(\frac {r} {100}\)

r = 10% P.a

**4. A man buys a TV by making cash down payment of Rs. 4945 and agrees to pay two more yearly installments of equivalent amounts at the end of first year and second year. If the rate of interest is 7 \(\frac {1} {2}\)% per annum, compounded annually, the cash value of the TV (in Rs.) is nearest to**

**Answer –** Option C

**Explanation –**

Let c be the cost of T.V.

c = 4945 \(( 1 + \frac {1} {1.075}+ \frac {1} {{1.075}^{2}})\)

= 4945 + 4600 + 4279 = 13824

**5. A sum of Rs.5000 amounts to Rs 8640 at compound interest in a ain times, then the same sum
amounts to what in one-third of the time?**

**Answer –** Option B

**Explanation –**

8640 = 5000 \(({1 + \frac {r} {100}})^{T}\) …….(i)

k = 5000 \(({1 + \frac {r} {100}})^{\frac{T}{3}}\)

cubing both sides

\({k}^{3}\) = \({5000}^{3}\) \(({1 + \frac {r} {100}})^{T}\) …….(ii)

Divide (1) and (2)

\({k}^{3}\) = \({5000}^{2}\) * 8640

k = 6000

**6. A loan of Rs.62496 is to be paid back in three equal annual installments. I f the inter est is compounded annual ly at 12 \(\frac {1} {2}\) %, t hen each installments will be of (in Rs.)**

**Answer –** Option B

**Explanation –**

Let equal instruments be of Ps. x

x(\({1.125})^{2} + 1.125 + 1\) = 62496 \(({1.125})^{3}\)

i.e, x = 26244

**7. Two equal sum are lent out at 6 % and 5% simple interest per annum respectively at the same time. The first is recovered 24 years earlier than the second one and the amount received in each case was Rs. 28800. Each sum (in Rs.) was**

**Answer –** Option A

**Explanation –**

Let each sum be Rs. x

According to the question

\(\frac {x * 6* (t – 24)} {100}\) = \(\frac {2 * 5 * t} {100}\)

Also, x + \(\frac {x * 5 * f} {100}\) = 28800

x = 18,000

**8. A computer is available for Rs. 22750 cash payment or for Rs. 6200 cash down payment and three equal annual installments of Rs. x. If the interest charged is 10% per annum. Compounded annually, the value of x is**

**Answer –** Option D

**Explanation –**

(22750 â€“ 6200) \( {(1.2)}^{3}\) = x \( {(1.1)}^{2}\) + (1.1) + 1

x = 6655

**9. A sum of money at simple interest amounts to Rs.13800 in 3 years . If rate of interest is increased by 30%,the same sum amounts to Rs.14340 in the same time. The rate of interest per annum is**

**Answer –** Option C

**Explanation –**

\(\frac {P * (1.3r) * 3} {100}\) – \(\frac {P * r * 3} {100}\) = 540

Pr = 60000

Also, P + \(\frac {P * r * 3} {100}\) = 13,800

r = 5%

**10. A person borrowed some money on compound interest and returned it in three years in equal annual installments. If the rate of interest in 15% per annum and the annual installment is Rs.48668, then the sum borrowed was (in Rs )**

**Answer –** Option C

**Explanation –**

Let money borrowed be Rs. x

According to the question

48668 (\({1.5})^{2} + 1.15 + 1\) = x \(({1.15})^{3}\)

x = 111120

**11. A sum of Rs. x at simple interest amounts to Rs. 14160 i n 3 year s. If the rate of interest is increased by 25 % the same sum amounts to Rs.14700 in the same time. The value of x is**

**Answer –** Option A

**Explanation –**

According to the question

\(x + \frac {x * r* 3} {100}\) = 14160 ….(1)

\(x + \frac {x *(r + \frac{r}{4}) * x3} {100}\) = 14700 ….(2)

solving (1) & (2)

i.e, x =12000.

**12. A certain sum of many is borrowed at compound interest for 3 year s at 5% per annum. The interest for the third year is greater than that of second year by Rs.642.60. t he sum (in Rs.) borrowed is**

**Answer –** Option C

**Explanation –**

I = Interest

\( {n}_{1st year}\) = \(\frac {P} {20}\)

\( {n}_{2nd year}\) = \(\frac {P} {20} + \frac {P} {400} +\frac {21P} {400}\)

\( {n}_{3nd year}\) = \(\frac {P} {20} + \frac {P} {400} + \frac {21P} {20 * 400}\)

\(\frac {4P} {8000}\) = 642.6

i.e, P = 244800

**13. A sum of Rs. 129780 is be paid back in three equal half yearly installments. If the interest is compounded half yearly at the rate of 3 \(\frac {1} {3}\)% per annum, then each installment is of Rs.**

**Answer –** Option D

**Explanation –**

Let each installment be Rs. x

\((129780) {(1.0665)}^{3}\)

x (\( {1.0665}^{2} + (1.0665) + 1\))

x = 49152

**14. A loan of Rs. 26480 is to be paid back in three equal yearly installment s. If the interest is compounded yearly at 10% per annum, then each installment is of Rs.**

**Answer –** Option C

**Explanation –**

(26480) \( {1.1}^{3}\)

(\( {1.1}^{2} + (1.1) + 1\))x

x = 10648

**15. A sum of Rs.78060 is divided between A and B, so that the amount of A after 3 \(\frac {1} {2}\) years is equal to the amount of B after 4 \(\frac {1} {2}\) year, the interest is compounded half yearly at 8% per annum. The share of B in the given sum is (in Rs.)**

**Answer –** Option D

**Explanation –**

Let sum with B = x

i.e, sum with A = (78060 â€“ x)

According to the question

\((1 + \frac {4} {100})^{9}\) = (78060 – X) \((1 + \frac {4} {100})^{7}\)

x\((1 + \frac {4} {100})^{2}\) = 78060 – x

x = 37500