8th Compound Interest Solved problems

Ex.1. Find compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually.

  Sol.  Amount = Rs [7500*(1+(4/100)2] = Rs (7500 * (26/25) * (26/25)) = Rs. 8112.            

            Therefore, C.I. = Rs. (8112 - 7500) = Rs. 612.

Ex. 2. Find compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually.

   Sol.         Time = 2  years  4  months = 2(4/12) years = 2(1/3) years.
                    Amount = Rs'. [8000 X (1+­(15/100))2 X (1+((1/3)*15)/100)]

                         =Rs. [8000 * (23/20) * (23/20) * (21/20)]     = Rs. 11109.                             .

                   :. C.I. = Rs. (11109 - 8000) = Rs. 3109.

    Ex. 3. Find the compound interest on Rs. 10,000 in 2 years at 4% per annum, the   interest being compounded half-yearly

Class 8th maths Test paper chapter COMPOUND INTEREST

1. Calculate the amount and compound interest on

(a) Rs 10,800 for 3 years at 12.5% per annum compounded annually (b) Rs 18,000 for 2.5 years at 10% per annum compounded annually(c) Rs 62,500 for 1.5 years at 8% per annum compounded half yearly.(d) Rs 8,000 for 1 year at 9% per annum compounded half yearly(e) Rs 10,000 for 1 year at 8% per annum compounded half yearly.

2. Kamala borrowed Rs 26,400 from a Bank to buy a scooter at a rate of 15% p.a. compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan?

3. Fabina borrows Rs 12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much?

4. I borrowed Rs 12,000 from Jamshed at 6% per annum simple interest for 2 years. Had I borrowed this sum at 6% per annum compound interest, what extra amount would I have to pay?

5. Vasudevan invested Rs 60,000 at an interest rate of 12% per annum compounded half yearly. What amount would he get (i) after 6 months? (ii) after 1 year?

6. Arif took a loan of Rs 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after 1.5 years if the interest is (i) compounded annually. (ii) compounded half yearly.

7. Maria invested Rs 8,000 in a business. She would be paid interest at 5% per annum compounded annually. Find (i) The amount credited against her name at the end of the second year. (ii) The interest for the 3rd year.

Class 8th maths Test paper chapter COMPOUND INTEREST: 1. Calculate the amount and compound interest on (a) Rs 10,800 for 3 years at 12.5% per annum compounded annually (b) Rs 18,000 for 2.5 ye...

CBSE SAMPLE PAPER MATHEMATICS (Class-8)

CBSE TEST PAPER 8TH MATHEMATICS SA-1

1. What least number must be subtracted from 7250 to get a perfect square? Also, find the square root of this perfect square

2. What is the least number by which 12348must be divided to obtain a perfect square?

3. Find the cost of erecting a fence around a square field whose area is 9 hectares if fencing costs  Rs 3.50 

per metre

4. Find the least number of six digits which is a perfect square. Find the square root of this number.

5. Divide   (1)    x³ - 1 by x - 1    (2)     7 +15x -13x² +5x³ by 4 - 3x + x²

6. .  x+ y + z = 0, prove that x ³+ y³ + z³ = 3xyz.  Or, Factorize :  (a⁸ – b⁸)

7.  If ( x² + 1/x2) = 83 .  Find   X3- 1/X3

Or, , Factorize  (i) 25a² – 4b² + 28bc – 49c²     (ii) 5y² – 20y – 8z + 2yz          8. A motor boat covers a certain distance downstream in a river in 5 hours. It covers the same distance 

upstream in 6 hours. The speed of water is 2 km/hr . Find the speed of the boat in still water.

9. Three prizes are to be distributed in a quiz contest. The value of the second prize is five sixths the value of 

the first prize and the value of the third prize is four – fifths that of the second prize. If the total value of three 

prizes is Rs. 150, find the value of each prize.

10. (a) Each side of a triangle is increased by 10 cm. If the ratio of the perimeters of the new triangle and the 

given triangle is 5 : 4, find the perimeter of the given triangle

(b) The difference between two positive integers is 36. The quotient, when one integer is divided by the 

other is 4. Find the two integers.

11. Factorize

(1 x⁴ – (y + z)⁴                             (2) y² –7y +12                                    (3) 6xy – 4y + 6 – 9x

(4)  a⁴ – 2a²b² + b⁴                            (5)  (x² – 2xy + y²) – z²       

8th Factorization

1. Factorization

(1)   (a + b ) (1 – c ) – (b + c ) ( 1 – c ) 

 (2)  1 6 a²   +  40 a b  + 25 b²          

(3)  4x²/9  - 2/3 x y +  y² /4

(4)    5x²yz   -    5 x³y    

(5)   18 q² + 338 p² -  1 5 6 p q        

 (6)  -108 x² -  363 y² + 369 x y   

2.  Factorize  

(1)  16- 4x²                                        

(2)   20 x³ – 45 b⁴x               

(3)     4a² –  9 b²  –  c²  -  6bc

4)  25 ( x + 2y )²  - 36 (2x-5y)²           

(5)   a² +  2 a b + b² – c2 -2cd –d²

3. Factorize using a²+b²+c² +2ab+2bc+2ca

(1)  x² + y² + 25 z² – 2 x y – 10 y z + 10 z x

(2)  9x²  +  4y² + 49z² –  12 x y  +  28 y z – 42  z x 

(3)   4x⁶ + 9y⁶ + 16 x ⁶ + 12 x³ y³ + 16 x³ z³ + 24 y³z³  

 (4)  a⁸ + 256 b⁸ + 96 a⁴b⁴-16a³b² – 256a²b⁶

4. Factorize (x + a) (x + b) = x² + (a + b) x +a b

(1) x²+7x+ 10 

(2) x²+x-20  (3) x²-4x-21    

(4) 15x² + 13x + 2       

 (5) -6x² - 13x+5

5. Factorize

(1) 125 a³ + 150 a²b + 60 ab³ + 8ab³            

 (2)  x⁶ – 12 x⁴ b⁴ c + 6a²b⁵c² + b⁶c³  

(3) 81a³ + 24b³          

(4) 64a³b² – 125 b⁵   (5)  16 a³ – 54 b³      

(6)  8X + 1  (7) –a³  - 27b³  (8) 729a⁶ - 1

 (9) 8m³ + 64    (10) 1000 – 343 a⁹

6. Find the following products:

(1)  (9m + 2m  )( 81m² -18mn + 4n²)       

 (2) (5 - 2x ) (25 +10x + 4x²)      

(3) (3 + 5/x ) ( 9 – 15/x + 25/x²)

7. Find the value of  27x² + 64y² + 36xy(3x + 4y) , when x = 5 and y = -3.

8. Using the identity (x + a) (x + b) = x²  + (a + b)x + a b, evaluate  98 ´ 97

9.  x + y + z = 0, prove that x ³+ y³ + z³ = 3xyz.

10. Factorize   

(1)  m⁴ – 256                           

(2) y² –7y +12                          

 (3) 6xy – 4y + 6 – 9x    

(4)  x⁴ – (y + z)⁴                             

(5) a⁴ – 2a²b² + b⁴                            

(6) (l + m) ² – 4lm

(7) (x² – 2xy + y²) – z²            

 (8) 25a² – 4b² + 28bc – 49c²      

(9) 5y² – 20y – 8z + 2yz   

(10) a⁸ – b⁸

8th Linear Equations In One and two Variable

1. The perimeter of a rectangular swimming pool is 154 metres. Its length is 2m more than twice its breadth. 

What are the length and breadth of the pool.

2. Sum of two numbers is 95. If one exceeds the other by 15 find the numbers.

3. Two numbers are in the ration 5:3. If they differ by 18, find these numbers

4. Three consecutive integers add up to 51. What are these integers?

5. The sum of three consecutive multiples of 8 is 888. Find the multiple.

6. Three consecutive integers are as such when they are taken in increasing order and multiplied by 2, 3, and 

4 respectively, they add up to 74. Find these numbers.

7. The number of boys and girls in a class is in 7:5 ratio. The number of boys is 8 more than that of girls. Fin 

their numbers.

8. The ages of Rahul and Haroon are in the ratio of 5:7. Four years from now sum of their ages will be 56 

years. Find their present age.

9. Baichung’s father is 26 years younger than Baichung’s grandfather and 29 years older than Baichung. The 

sum of their ages is 135. Find their ages.

10. Fifteen years from now Ravi’s age will be 4 times his current age. What is his current age.

11. Lakshmi is a cashier in a bank. She has notes of denominations of Rs. 100, 50 and 10 respectively. The 

ratio of number of these notes is 2:3:5 respectively. The total cash with Lakshmi is 4,00,000. How many 

notes of each denomination does she have?

12. I have total Rs 300 in coins of denominations of Rs.1, Rs.2, and Rs. 5.The number of Rs. 2 coins is 3 

times the number of Rs. 5 coins. The total number of coins is 160. How many coins of each denomination 

are with me.

13. The organizers in an essay competition decide that winner will get a prize of Rs. 100 and a participation 

who doesn’t win gets a prize of Rs. 25. The total prize money distributed is Rs. 3,000. Find the number of 

winners if the total number of participants is 63.

14. If in a rational number denominator is greater than numerator by 8. If you increase the numerator by 17 

and decrease the denominator by 1, you get 3/2 as result. Find the number.

15. Amina thinks of a number and subtracts 5/2 from it. She multiplies the result by 8. The final result is 3 

times her original number. Find the number

16. A positive number is 5 times another number. If 21 is added to both the numbers then one of the new 

numbers becomes twice of another new numbers. Find the original numbers.

17. Sum of the digits of a two digit number is 9. When we interchange the digits the new number is 27 

greater than the earlier number. Find the number.

18. One of the digits of a two digit number is three times the other digit. If you interchange the digits and add 

the resulting number to original number you get 88 as final result. Find the numbers.

19. Sahoo’s mother’s present age is six times Sahoo’s present age. Five year from now Sahoo’s age will be 

one-third of his mother’s age. Find their current age.

20. There is a narrow rectangular plot. The length and breadth of the plot are in the ratio of 11:4. At the rate 

of Rs. 100 per metre it will cost village panchayat Rs.75000 to fence the plot. What are the dimensions of 

the plot.

21. Hasan buys two kinds of cloth materials for school uniform. Shirt material cost him Rs. 50 per metre and 

trousers material cost him Rs. 90 per metre. For every 2 metres of the trousers material he buys 3 metres of 

shirt material. He sells them at 12% and 10% profit respectively. His total sale is Rs. 36,660. How much 

trousers material did he buy? ( 200m)

22. Half of a herd of deer are grazing in the field and three fourths of the remaining are playing nearby. The 

rest 9 are drinking water from the pond. Find the total number of deer in the herd.

23. A grandfather is 10 times older than his granddaughter. He is also 54 years older than her. Find their age.

24. A man’s age is three times his son’s age. Ten years ago his age was five times his son’s age. Find their 

current age.

 25. Hari and Harry’s age are in the ratio of 5:7. Four years later the ratio of their ages will be 3:4. Find their 

current age.

8th Algebraic Expression & Compound Interest