# simple and compound Intrest questions and solutions

**simple and compound Intrest questions and solutions**

**Question :**A sum of money amounts to Rs.53200 at 11% simple interest in 3 years. Find the sum.

Option 1 : Rs.40000

Option 2 : Rs.38900

Option 3 : Rs.33100

Option 4 : Rs.17024

Answer : A

**Explanation :**Let the sum be Rs.x

SI = x*11*3/100

= 33x/100

P+SI = A

x+(33x/100) = 53200

133x = 5320000

x=40000

**Question :**A sum of Rs.20000 is compounded annually at an interest rate of 10%. How much does it amount to after 2 years?

Option 1 : Rs.24420

Option 2 : Rs.24400

Option 3 : Rs.24000

Option 4 : Rs.24200

Answer : D

**Explanation :**A = P[1+(R/100)]^n

= 20000[1+(10/100)]²

= 20000[1.1]²

= 20000*1.21

= Rs.24200

**Question :**I borrowed two equal amounts, one at 12% S.I. for 2 years and the other at 10% for 3 years respectively. If the difference in the interest was Rs.1200 , find the total amount borrowed.

Option 1 : Rs.20000

Option 2 : Rs.30000

Option 3 : Rs.40000

Option 4 : Rs.50000

Answer : C

**Explanation :**Let the amount borrowed be Rs.x

SI on the first amount

= 12*2*x/100

= 24x/100

SI on the second amount

= 10*3*x/100

= 30x/100

Difference in the interests

= 6x/100 = 1200

Solving,

x=Rs.20000

Total amount

=Rs.40000

**Question :**A sum of Rs.50000 was divided into two parts and the first part was deposited at 10% simple interest and the second part at 8% interest. At the end of two years, the interest earned was Rs.8800 . Find the amount deposited at 8% interest.

Option 1 : Rs.20000

Option 2 : Rs.30000

Option 3 : Rs.25000

Option 4 : Rs.24000

Answer : B

**Explanation :**Let the sum be divided into Rs.x and Rs.y

x+y=50000

x=50000-y

Interest on the first part

= x*2*10/100

= 20x/100

Interest on the second part

= y*2*8/100

= 16y/100

Total interest

[(20(50000-y))+16y]/100 = 8800

1000000-20y+16y=880000

4y=120000

y=30000

**Question :**Find the simple interest on a sum of Rs.80000 at 8% interest for 8 years.

Option 1 : Rs.51200

Option 2 : Rs.64000

Option 3 : Rs.6400

Option 4 : Rs.8000

Answer : A

**Explanation :**SI=PTR/100

=80000*8*8/100

=51200

**Question :**If the compound interest on a certain sum at 5% for 2 years is Rs.512.50, what would be the simple interest?

Option 1 : Rs.500

Option 2 : Rs.510

Option 3 : Rs.450

Option 4 : Rs.512.5

Answer : A

**Explanation :**A = P[1+(R/100)]²

P+512.5 = P*(105/100)²

P+512.5 = 1.1025P

0.1025P = 512.5

P=5000

SI = 5000*2*5/100 = Rs.500

**Question :**The compound interest on a certain sum at a certain rate of interest for the 1st year is Rs.1200 and for the 2nd year is Rs.1344. Find the rate of interest.

Option 1 : 12.5%

Option 2 : 8%

Option 3 : 12%

Option 4 : 10%

Answer : C

**Explanation :**At the end of 1 year,

A = P[1+(R/100)]

P+1200 = P+(PR/100)

PR = 120000

At the end of 2 years,

A = P[1+(R/100)]²

P+1200+1344 = P+(2PR/100)+(PR²/10000)

Substitute PR=120000,

2544 = (2*120000/100)+(120000R/10000)

Solving,

R=12%

**Question :**Rs.20000 is invested at 11% compound interest for 2 years. Find the interest in the second year.

Option 1 : Rs.4642

Option 2 : Rs.2200

Option 3 : Rs.4400

Option 4 : Rs.2442

Answer : D

**Explanation :**After 1 year,

A = 20000[1+(11/100)]

= Rs.22200

I = Rs.2200

After 2 years,

A = 20000[1+(11/100)]^2

= Rs.24642

I = Rs.4642

Interest in the second year

= 4642-2200

= Rs.2442

**Question :**A borrows an amount of Rs.15000 from B at 8% simple interest and lends it to C at 10% interest. How much does B gain after 2 years?

Option 1 : Rs.1500

Option 2 : Rs.600

Option 3 : Rs.200

Option 4 : Rs.400

Answer : B

**Explanation :**Interest paid by B to A

= 15000*2*8/100

= 2400

Interest paid by C to B

= 15000*2*10/100

= 3000

B gains Rs.600.

Alternatively, B gains (10-8)=2% of 15000.

**Question :**On simple interest, a sum of Rs.5000 amounts to Rs.6200 in 3 years at a given rate of interest. How much would it amount to if the interest rate is increased by 2%?

Option 1 : Rs.6725

Option 2 : Rs.6800

Option 3 : Rs.7500

Option 4 : Rs.6500

Answer : D

**Explanation :**Interest=Rs.1200

I=PTR/100

1200=5000*3*R/100

R=8%

R1=10%

I1=5000*3*10/100

= 1500

A1=Rs.6500

**Question :**Amar and Amit divide Rs.100000 between them and deposit it in a bank at 8% simple interest. At the end of 5 years, Amar's share is R.28000 more than that of Amit. Find the ratio in which they divided the original amount.

Option 1 : 3:2

Option 2 : 5:4

Option 3 : 4:3

Option 4 : 5:3

Answer : A

**Explanation :**Let Amar's original share be P1 and Amit's share be P2.

P1+P2=100000

SI1 = P1*5*8/100

= 0.4P1

A1 = P1+SI1

= 1.4P1

SI2 = 0.4P2

A2 = 1.4P2

A1 - A2 = 28000

1.4P1-1.4P2=28000

P1-P2=20000

P1+P2=100000

Solving,

P1=60000

P2=40000

P1:P2=3:2

**Question :**How long does it take for a sum of Rs.2500 to become Rs.12500 at 10% simple interest?

Option 1 : 40 years

Option 2 : 50 years

Option 3 : 25 years

Option 4 : 49 years

Answer : A

**Explanation :**SI = PTR/100

= 2500*T*10/100

= 250T

P+SI = A

2500+250T = 12500

10+T = 50

T = 40 years

**Question :**The rate of growth of population of a village has been compounding annually at a constant rate of 5%. If the present population of the village is 10000, find the population after two years.

Option 1 : 10500

Option 2 : 11025

Option 3 : 15000

Option 4 : 10250

Answer : B

**Explanation :**The current population is taken as P.

Population after 2 years

= 10000[((1+(5/100))²]

= 11025

**Question :**The difference between the compound and simple interest on Rs.40000 for 2 years at the same rate of interest is Rs.400. Find the rate of interest.

Option 1 : 12%

Option 2 : 4%

Option 3 : 8%

Option 4 : 10%

Answer : D

**Explanation :**SI = 40000*2*R/100

= 800R

CI = [40000(1+(R/100))²]-40000

= 40000[(1+(R/100))²-1]

= 40000[1+(2R/100)+(R²/10000)-1]

= 800R+4R²

CI-SI = 400

4R²+800R-800R = 400

R²=100

R=10%

**Question :**A sum of Rs.7500 at compound interest at 4% per annum for 2 years amounts to

Option 1 : Rs.7800

Option 2 : Rs.8100

Option 3 : Rs.8112

Option 4 : Rs.8082

Answer : C

**Explanation :**A = P[1+(R/100)]^n

= 7500[[1+4/100]²

= 7500[1.04]²

= Rs.8112

**Question :**An amount increases by 40% in 5 years at simple interest. By how much % does it increase in 2 years at the same rate on compound interest?

Option 1 : 21%

Option 2 : 17.28%

Option 3 : 16.64%

Option 4 : 13.31%

Answer : C

**Explanation :**S.I = 0.4P = P*5*R/100

R=8%

A = P[1+(8/100)]^2 = P[1.08]^2 = 1.1664P

It increases by 16.64%

**Question :**At what rate of compound interest will a sum of Rs.8000 amount to Rs.8820 in two years?

Option 1 : 8%

Option 2 : 10%

Option 3 : 6%

Option 4 : 5%

Answer : D

**Explanation :**8820 = 8000[(1+(R/100))²]

[1+(R/100)]² = 8820/8000 = 1.1025 = (1.05)²

R = 5%

**Question :**Simple interest on Rs.3500 for 2 years at 9% interest is equal to the compound interest on a certain sum of money for the same number of years at 10% per annum. Find the sum of money.

Option 1 : Rs.3310

Option 2 : Rs.3000

Option 3 : Rs.3500

Option 4 : Rs.6300

Answer : D

**Explanation :**S.I = 3500*2*9/100 = Rs.630

C.I = P[(1+(10/100))^2] – P

= P[(1.1)^2 – 1]

= 0.21P

= 630

P = Rs.3000

**Question :**If the simple interest on a certain sum of money for 3 years at 10% interest is Rs.300, find the compound interest on the same sum for the same time at the same rate of interest.

Option 1 : Rs.300

Option 2 : Rs.321

Option 3 : Rs.210

Option 4 : Rs.331

Answer : D

**Explanation :**P = 300*100/(3*10) = Rs.1000

A = 1000*(1+(10/100))^3 = 1331

C.I = 1331-1000 =Rs.331

**Question :**The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is

Option 1 : 3

Option 2 : 4

Option 3 : 5

Option 4 : 6

Answer : B

**Explanation :**A>2P

P((1+(20/100))^n) >2P

(1.2)^n>2

By trial and error,

1.2^2=1.44

1.2^3=1.728

1.2^4=2.0736

Least possible value of n=4

**Question :**Ram and Shyam deposit an equal amount of money in a bank at simple interest. Ram deposits for a time thrice as long as Shyam at two-thirds of Shyam’s interest rate. Find the ratio of the interests received by Ram and Shyam.

Option 1 : 2:3

Option 2 : 2:1

Option 3 : 3:2

Option 4 : 1:2

Answer : B

**Explanation :**Let the amount be Rs.P

Interest received by Shyam

= P*T*R/100

Interest received by Ram

=[ P*3T*(2/3)R]/100

= 2PTR/100

Ram’s Interest:Shyam’s Interest = 2:1

**Question :**A finance company claims to lend money at simple interest, but includes the interest every six months for calculating the principal. If they charge an interest of 8%, what is the effective rate of interest?

Option 1 : 8.5%

Option 2 : 8%

Option 3 : 8.16%

Option 4 : 9%

Answer : C

**Explanation :**Consider a sum of Rs.100

Interest for the first 6 months

= 100 * ½ *8/100

= Rs.4

Interest for the next 6 months

= 104 * ½ *8/100

= Rs.4.16

Interest at the end of 1 year

= Rs.8.16 for a sum of Rs.100

Effective rate of interest = 8.16%

**Question :**The difference between compound interest and simple interest on a sum of Rs.10000 for 2 years at a rate of 5% interest is

Option 1 : Rs.25

Option 2 : Rs.20

Option 3 : Rs.10

Option 4 : Rs.5

Answer : A

**Explanation :**S.I = 10000*2*5/100 = 1000

C.I = [10000(1+(5/100))^2)] - 10000 = 1025

C.I-S.I = Rs.25

**Question :**A lends a sum of Rs.15000 to B at an interest rate of 8%. B uses Rs.5000 and he lends the remaining amount to C. At what rate should B lend the amount to C so that the interest received by B will equal the interest payable by B to A?

Option 1 : 8%

Option 2 : 10%

Option 3 : 12%

Option 4 : 24%

Answer : C

**Explanation :**15000*T*8/100 = 10000*T*R/100

R = 15*8/10 = 12%

**Question :**A sum of money amounts to Rs.49440 in three years and Rs.50400 in five years at the same interest rate. Find the rate of interest per annum.

Option 1 : 10%

Option 2 : 9%

Option 3 : 9.6%

Option 4 : 8%

Answer : A

**Explanation :**Interest for 2 years

= 50400-49440

= Rs.960

Interest for 3 years

= 3*960/2

= Rs.1440

Principal = 49440-1440 = Rs.48000

1440 = 48000*3*R/100

R=10%

**Question :**Ganesh lends an amount of Rs.15000 to Arun for 3 years and an amount of Rs.25000 to Varun for 2 years at the same interest rate. The total interest received by him is Rs.9500. Find the rate of interest.

Option 1 : 7%

Option 2 : 8%

Option 3 : 9%

Option 4 : 10%

Answer : D

**Explanation :**(15000*3*R/100)+(25000*2*R)/100 = 9500

Solving this, R=10

**Question :**How many years does it take for an amount of Rs.20000 to fetch an interest of Rs.8400 at 7% interest?

Option 1 : 5 years

Option 2 : 5.5 years

Option 3 : 6 years

Option 4 : 7 years

Answer : C

**Explanation :**I = PTR/100

8400 = 20000*T*7/100

T=6

**Question :**A sum of money fetched an interest of Rs.3840 in 4 years at an interest rate of 8%. Find the sum.

Option 1 : Rs.8000

Option 2 : Rs.12000

Option 3 : Rs.16000

Option 4 : Rs.19200

Answer : B

**Explanation :**I = PTR/100

3840 = P*4*8/100

P = Rs.12000

**Question :**On Simple Interest, a given sum amounts to an interest equal to 9/25 of the sum. Find the rate of interest if it is numerically equal to time.

Option 1 : 3%

Option 2 : 4%

Option 3 : 5%

Option 4 : 6%

Answer : D

**Explanation :**I = P*T*R/100

(9/25)P = P*R*R/100

R = 6%

**Question :**Ram lends a sum of money to Shyam at an interest rate of 5% p.a. After two years, he charges an interest of 8% p.a. At the end of five years, Shyam pays Rs. 13400 to Ram, how much money did he initially borrow?

Option 1 : Rs.8000

Option 2 : Rs.9000

Option 3 : Rs.10000

Option 4 : Rs.10500

Answer : C

**Explanation :**Let the sum of money be Rs.x

Total Interest

= (x*2*5/100) + (x*3*8/100)

= 0.34x

x+0.34x = 1.34x = 13400

x = Rs.10000

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