2. maths
Project work

3. Chapter : 8
Comparing quantities

4. Exercise : 8.1
q.1: Find ratio of the following : (a): Speed of a cycle 15 km per hour to the speed of scooter 30 km per hour . Sol : Ratio = 15 km : 30 km = 15 : 30 = 15/30 = 1/2 = 1 : 2

5. Sol : Ratio = 5 m : 10 km = 5 m : 10000 m = 5 : 10000 = 5/10000
(b) : 5 m to 10 km .
Sol : Ratio = 5 m : 10 km
= 5 m : m
= 5 : 10000
= 5/10000
= 1/2000
= 1 : 2000

6. (c) : 50 paise to Rs 5 . Sol : Ratio = 50 paise : Rs 5 = 50 paise : 500 paise = 50 : 500 = 50/500 = 1/10 = 1: 10

7. Q.2 : Convert the following ratio to % : (a) : 3 : 4 Sol : 3 : 4 % = 3/4 = 3/4 x 100 = 75 % 2 : 3 Sol : 2 : 3 % = 2/3 = 2/3 x 100 = 66 2/3 %
(b) :

8. Q. 3 : 72 % of 25 students are good in Mathematics
Q.3 : 72 % of 25 students are good in Mathematics . How many are not good in Mathematics ? Sol : No. of st. good in maths = 75 % No. of st. not good in maths = (100 – 72) = 28 % of 25 = 28/100 x 25 = 7 st.

9. Q. 4 : A football team won 10 matches out of the total no
Q.4 : A football team won 10 matches out of the total no. of matches they played . If their win % was 40 , then how many matches did they play in all ? Sol : Let they played games in all be x . The no. of games won by f.b. t.= 40% of x = 40/100 x (x) = 2x According to the Q. : 2x/5 = 10 x = 10 x 5/2 = 25 Therefore, 7 st. are not good in Mathematics.

10. Q.5 : If Chameli had Rs 600 left after spending 75% of her money, how much did she have in the beginning ? Sol : let the t.money she had in the beginning was Rs x. The money she had spent = 75% of Rs x = 75/100 x (x) = Rs 3x/4 Money she had left = Rs x – Rs 3x/4 = Rs {x – 3x/4} = Rs x/4

11. According to the question ; x / 4 = 600 x = 600 x 4 = Rs 2400 Therefore , the money she had in the beginning was Rs

12. q.6 : If 60% people in a city like cricket, 30% like football and the remainig like other games then what % of the people like other games ? If the total no. of people are 50 lakh, find the exact no. who like each type of game ? Sol :% of p. like o.game = [100 – (60+ 30)% = (100 – 90) % = 10 %

13. No. of people like cricket = 60 % of 50,00,000 = 60/100 x 50,00,000
Total no. of people = 50 lakh
= 50,00,000
No. of people like cricket = 60 % of 50,00,000
= 60/100 x 50,00,000
= 3,00,000= 3 lakh
No. of people like football = 30% of 50,00,000
= 30/100 x 50,00,000
= 15,00,000 = 15 lakh

14. No. of like people o. games = 10% of = 10/100 x = 5,00,000 = 5 lakh Therefore, 3 lakh people like cricket, 15 lakh people like football & 5 lakh people like other games .

15. Exercise : 8.2
Q.1 : A man got a 10% increase in his salary . If tis new salary is Rs 1,54,000, find his original salary ? Sol : Let his original salary be Rs (x) . Increase in his salary = 10% of Rs (x) =10/100 x (x) = Rs x/10

16. New salary = o. salary + i. salary = Rs x + Rs x/10 = Rs 11x/10 According to the question ; 11x/10 = (x) = x 10/11 (x) = 1,40,000 Therefore, his original salary is Rs 1,40,000.

17. Q. 2 : On Suday 845 people went to the Zoo. On Monday 169 people went
Q.2 : On Suday 845 people went to the Zoo. On Monday 169 people went . What is the % decrease in the visiting the Zoo on Monday? Sol : No. of people went to Zoo on Sunday = 845 people No. of people went to Zoo on Monday = 169 people

18. Decrease in no. of people visiting the Zoo = 845 – 169 ( people ) = 676 people % decrease in the no. of people visiting the Zoo = 676/845 x 100% = 80% Therefore, the % decrea % .se in the people visiting the Zoo on Monday is

19. Q.3 : A shopkeeper buys 80 articles for Rs 2,400 and sells them for a profit of 16 %. Find the selling price of one article ? Sol : C.P. of 80 articles = Rs 2,400 Profit = 16 % of Rs 2,400 = 16/100 x 2,400 = Rs 384

20. S. P. of 80 articles = C. P. + Profit = Rs 2,400 + Rs 384 = Rs 2,784 S
S.P. of 80 articles = C.P. + Profit = Rs 2,400 + Rs 384 = Rs 2,784 S.P. of 1 article = Rs 2,784/80 = Rs Therefore, the selling price of one article is Rs 34.80

21. q.4 : The cost of an article was Rs 15,500, Rs 450 were spent on its repairs . If it is sold for a profit of 15%, find the selling price of the article ? Sol : C.P. of an article = Rs 15,500 + Rs 450 = Rs 15,950 Profit = 15% of Rs 15,950 = 15/100 x 15,950 =Rs 2,392.50

22. S. P. of an article = C. P. + Profit = Rs 15,950 + Rs2,392
S.P. of an article = C.P. + Profit = Rs 15,950 + Rs2, = Rs 18, Therefore, the selling price of the article is Rs 18,342.50

23. q. 5 : A VCR and TV were bought for Rs 8,000 each
q.5 : A VCR and TV were bought for Rs 8,000 each. The shopkeeper made a loss of 4% on the VCR and a 8% on the TV. Find thegain or loss % on the whole transaction ? Sol : Combined C.P. of the both VCR and TV = Rs 8,000 + Rs 8,000 = Rs 16,000 Loss of 4% on the VCR = 4/100 x 8,000 = Rs 320

24. S.P. of the VCR = C.P. – Profit = 8,000 – 320 = Rs 7,680 Profit of 8% on the TV = 8/100 x 8,000 = Rs 640 S.P. of the TV = C.P. + Profit = 8, = Rs 8,640

25. Combined S.P. = Rs 7,680 + Rs 640 = Rs 16,320 Gain of the whole transaction = S.P. – C.P. = Rs 16,320 – Rs 16,000 = Rs 320 Gain % = 320/16,000 x100 = 2% Therefore, the gain % on the whole transaction is 2% .

26. q. 6 : During a sale, a shop offered a discount of 10% on th M. P
q.6 : During a sale, a shop offered a discount of 10% on th M.P. of all the items. What would a customer have to pay for a pair jeans marked at Rs 1,450 and two shirts marked at Rs 850 each ? Sol : M.P. of a pair of Jeans = Rs 1,450 M.P. of a Shirt = Rs 850 M.P. of the two Shirts = Rs (2 x 850) = Rs 1,700

27. Therefore, the customer will have to pay
T.M.P. of a pair of Jeans and Shirts
= Rs 1,450 + Rs 1,700
= Rs 3,150
Discount of 10% = 10/100 x 3,150
= Rs 315
S.P. = T.M.P. – Discount
= Rs 3150 – Rs 315
= Rs 2835
Therefore, the customer will have to pay
Rs 20,000 each for a pair of jeans and
two shirts .

28. q. 7 : A milkman sold two of his buffaloes for Rs 20,000 each
q.7 : A milkman sold two of his buffaloes for Rs 20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss ? Sol : C.P. of both the two buffaloes be (x) and (y) . S.P. of each buffalo = Rs 20,000 C.P. of the first buffalo = S.P. x 100/ = 20,000 x 100/105 = 4,00,000/21

29. C.P. of the second buffalo
= S.P. x 100/100 – 10
= 20,000 x 100/90
= 2,00,000/9
Over-all loss = C.P. – S.P.
= 4,00,000/21 + 2,00,000/9 – 40,000/1
= 12,00, ,00,000 – 25,20,000/63
= 80,000/63
= Rs 1,269.84

30. q.8 : The price of a TV is Rs 13,000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it ? Sol : C.P. of the T.V = Rs 13,000 Sales tax charged on it = 12% of 13,000 = 12/100 x 13,000 = Rs 1,560 S.P. = C.P. + Sales tax = Rs (13, ,560) = Rs 14,560

31. q.9 : Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is Rs 1,600, find the marked price ? Sol : Let the M.P. be Rs (x) . Discount of 20% = 20/100 x (x) = Rs x/5 S.P. = M.P. – Discount = Rs x – Rs x/5 = Rs 4x/5

32. Therefore, the M.P. of the pair of skates is Rs 2,000 .
According to the question ;
4x/5 = 1,600
x = 1,600 x 5/4
x = Rs 2,000
Therefore, the M.P. of the pair of skates
is Rs 2,000 .

33. q. 10 : I purchased a hair – dryer for Rs 5,400 including 8% VAT
q.10 : I purchased a hair – dryer for Rs 5,400 including 8% VAT. Find the price before VAT was added ? Sol : When the price including VAT is Rs 108 , Original price = Rs 100 When price including VAT is Rs 5,400 , Original price = Rs 100/108 x 5,400 = Rs 5,000 Therefore, the price before VAT was added is Rs 5,000

34. Exercise : 8.3
q.1 : Calculate the amount and compound interest on : (a): Rs 10,800 for 3 years at 12 ½ % per annum compounded anually . Sol : P : Rs 10,800 R : 12 ½ % = 25/2 % T : 3 years

35. n
A = P ( 1+R /200 )
= 10,
= 10,
= 10,
= 10,000 x 9 x 9 x 9 ( ) 1 3
200 8 ( ) 3 8 ( ) 3 8
672
1350 8 8 8 4 1

36. = 675 x 9 x 9 x 9
= 675 x 729
= 4,92,075
= Rs 15,377.34
C.P. = A – P = 15, – 10,800
= Rs 4,577.34 8 32 32

37. (b) : Rs 18,000 for 2 ½ year ay 10% per annum compounded annualy
(b) : Rs 18,000 for 2 ½ year ay 10% per annum compounded annualy . Sol : P ; Rs 18,000 R : 10% T : 2 ½ year A = P ( 1+R /100 ) = 18, = 18, n ( ) 2
100 ( ) 2 10

38. ( )
= 18, = 18,000 x 11 x 11 = 180 x 121 = Rs 21,780 S.I. = PRT = 21,780 x 10 x ½ = Rs 1,089 2 10 10 10
100

39. = Rs 3,80 T.C.I. = 3,780 + 1,089 = Rs 4,869 A of 2 ½ year = P + I
C.I. = A – P = 21,780 – 18,000
= Rs 3,80
T.C.I. = 3, ,089
= Rs 4,869
A of 2 ½ year = P + I
= 21, ,089
= Rs 22,869

40. (c) : Rs 62,500 for 1 ½ year at 8% per annum compounded half yearly
(c) : Rs 62,500 for 1 ½ year at 8% per annum compounded half yearly . Sol : P = Rs 62,500 R = 8% = 4 years T = 1 ½ year = 3 A = P 1 + R = 62, ( ) n
100 ( ) 3
100

41. ( ) 3
= 62,
= 62,
= 62,500 x 26 x 26 x 26
= 4 x 26 x 26 x 26
= Rs 70,304 25 ( ) 3 25 4
100
2,500 25 25 25 1 1 1

42. C.I. = A – P = 70,304 – 62,500 Rs 7,804

43. (d) : Rs 8,000 for 1 year at 9% per annum compounded half yearly
(d) : Rs 8,000 for 1 year at 9% per annum compounded half yearly . Sol : P = Rs 8,000 R = 9% = 9/2 T = 1 year A = P 1 + R = 8, ( ) n
200 ( ) 2
200

44. ( ) 2
= 8,
= 8,
= 8,000 x 209 x 209
= 2 x 209 x 209
= 47,362
200 ( ) 2
200 2 4
200
200 10 1 10 10

45. = Rs 8,736.2 C.I. = A – P = 8,736.2 – 8,000 = Rs 736.2

46. (e) : Rs 10,000 for 1 year T 8% per annum compounded half yearly
(e) : Rs 10,000 for 1 year T 8% per annum compounded half yearly . Sol : P = Rs 10,000 R = 8% = 4% T = 1 year = 2 A = P 1 + R = 10, ( ) n
100 ( ) 2 1
100 25

47. ( ) 2
= 10,
= 10,
= 10,000 x 26 x 26
= 16 x 26 x 26
= Rs 10,816 25 ( ) 2 25 16
100 25 25

48. C.I = A – p = 10,816 – 10,000 = Rs 816

49. q.2 : Kamala borrowed Rs 26,400 from a bank to buy a scooter at a rate of 15% p.a. compounded annually . What amount will she pay at the end of 2 years and 4 months to clear the loan ? Sol : P = Rs 26,400 R = 15% T = 2 years, 4 months = 2 y. and 1/3 y. = 2

50. ( ) 2
A = P 1+ R = 26, = 26, = 26, = 26,400 x 23 x 23
100 ( ) 2 3
100 20 ( ) 2 20 ( ) 2 20 66
132 20 20

51. = 66 x 23 x 23 = Rs 34,914 S.I. = PRT = 34,914 x 15 x 1 = 34,914 x 5 = 1,74,570 = Rs 1,745.70
100
100 x 3 1
100
100

52. T.A = 34, ,745.70
= Rs 36,659.70
C.I = A – P
= 36, – 26,400
= Rs 10,259.70

53. q. 3 : Fabina borrows Rs 12,500 at 12% per annum for 3 years at S
q.3 : Fabina borrows Rs 12,500 at 12% per annum for 3 years at S.I 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 ? Sol : For Fabina ; P = Rs 12,500 R = 12% T = 3 years

54. S.I = = 12,500 x 12 x 3 = 125 x 12 x 3 = Rs 4,500 For Radha ; P = Rs 12,500 R = 10% T = 3 years
PRT
100
100

55. ( ) n
A = P 1 + R = 12, = 12, = 12, =12,500 x 11 x 11 x 11
100 ( )
100 ( ) 3 10 ( ) 3 10 10 10 10

56. = 125 x 11 x 11 x 11 = 1,66,375 = Rs 1,66, C.I = A – P = 1,66, – 12, = Rs 4,137.50 10 10

57. Difference between C. I and S. I ; = 4,500. 00 – 4,137. 50 = Rs 362
Difference between C.I and S.I ; = 4, – 4, = Rs Therefore , Fabina pays more money by Rs than Radha .

58. q.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 coumpound , what exess amount would I have to pay ? Sol : P = Rs 12,000 R = 6% T = 2 years S.I = PRT = 12,000 x 6 x 2 = 120 x 12 = Rs 1,440
100
100

59. ( ) n
A = P R
= 12,
= 12,
= 12,
= 12,500 x 53 x 53
100 ( ) 2 3
100 50 ( ) 2 50 ( ) 2 50 24 50 50 1

60. = 24 x 53 x 53 = Rs 13, C.I = A – P = 13, – 12, = Rs 1, Excess A = 1, – 1, = Rs Therefore , I would have to pay to him an excess amoun of Rs 5

61. q.5 : Vasudevan invested Rs 60,000 at an interest rate of 12% per annum compouunded half yearly . What amount would he get (i) After 6 months ? Sol : P = Rs 60,000 R = 12% = 6% T = ½ year = 1 half year

62. ( ( n
A = P 1 + R = 60, = 60, = 60, = 60,000 x 106
100 ( ) 1
100 ( ) 1
100 ( ) 1
100
100

63. = 600 x 106 = Rs 63,600 There fore , he would get Rs 63,600 after 6 months .

64. (ii) : After 1 year ? Sol : P = Rs 60,000 R = 12% = 6% T = 1 year = 2 A = P 1 + R = 60,000 1 + 6 n
100 ( ) 3 2
100 50

65. ( ) 2
= 60, = 60, =60,000 x 53 x = 120 x 53 x 53 = 24 x 53 x 53 = Rs 67,416 50 ( ) 2 50
120 1 24 5 1

66. q. 6 : Arif took a loan of Rs 80,000 frm a bank
q.6 : Arif took a loan of Rs 80,000 frm a bank . If the rate of interest is 10% per annum , find the difference in amounts he would be paying after 1 ½ years if the interest is ; (i) : Compounded annually ? Sol : P = Rs 80,000 R = 10% T = 1 ½ year = 1 year

67. ( ( n
A = P R
= 80,
= 80,
= 80,
= 80,000 x 11
100 ( ( 1
100 ( 1 ( 10 ( 1 ( 10 10

68. = 8,000 x 11 = Rs 88,000 S.I = PRT = 88,000 x 10 x 1 = Rs 4,400
4,400
100
2 x 100 1

69. (ii) : Compounded half – yearly
(ii) : Compounded half – yearly ? Sol : P = Rs 80,000 R = 10% = 5% T = 1 ½ years = 3 A = P 1 + R = 80, ( ) n
100 ( ) 1 3
100 20

70. ( ( 3
= 80, = 80, = 80,000 x 21 x 21 x 21 = 10 x 21 x 21 x 21 = Rs 92,610 20 ( ( 3 20 10 20 40 1 1 1

71. q. 7 : Maria invested Rs 8,000 in a business
q.7 : Maria invested Rs 8,000 in a business. She would be paid interest at rate of 5% per annum compounded annually . Find ;
: The amount credit against her name at the end of the second year .
Sol : P = Rs 8,00
R = 5%
T = 2 years
A = P R ( n (
100

72. ( ( 1 2
= 8, = 8, = 8, = 8,000 x 21 x 21 = 20 x 21 x 21 = Rs 8,820
100 20 ( ( 2 20 ( ( 2 20 20
400 20 20 1 1

73. (ii) : The interest for the third year
(ii) : The interest for the third year . Sol : P = Rs 8,820 R = 5% T = 1 years A = P 1 + R = 8, = 8, ( ( n
100 ( ( 1 1
100 20 ( 1 ( 20

74. ( ( 1
= 8, = 8,820 x 21 = 441 x 21 = Rs 9,261 20
441 20 1

75. q.8 : Find the amount and the compound interest on Rs 10,000 for 1 ½ years at 10% per annum, compounded half yearly . Would this interest be more than the interest he would get if it was compounded annually ? Sol : P = Rs 10,000 R = 10% = 5% T = 1 ½ years = 3

76. Compounded haif - yearly A = P 1 + R = 10,000 1 + 5 = 10,000 20 + 1 = 10,000 21 ( ) n
100 ( ) 3 1
100 20 ) ( 3 20 ( ) 3 20

77. = 10,000 x 21 x 21 x 21 = Rs 11, C.I = A – P = 11, – 10,000 = Rs 1, There fore , the interest when compounded half yearly would be more than the interest when compounded annually . 20 20 20

78. q.9 : Find the amount which Ram will get on Rs 4,096 , if he gave it for 18 months at 12 ½ years per annum , interest being compounded half - yearly ? Sol : P = Rs 4,096 R = 12 ½ % = 25/2% =1/2 x 25/2% = 25/4% T = 18 months = 3 A = P 1 + R ( ) n
100

79. ( ) 3
= 4, = 4, = 4, = 4, = 4,096 x 17 x 17 x 17
4 x 100 ( ) 1 3
400 16 ( ) 3 16 ( ) 3 16 16 16 16

80. = Rs 4,913 There fore , the required amount is Rs 4,913 .

81. Muliple choise question

82. (a) : 20% (c) : 40% (b) : 30% (d) : 50%
q.1 : The fraction 2/5 converted to % age is:
(a) : 20% (c) : 40%
(b) : 30% (d) : 50%
Q.2 : The marked price of a book is Rs The shopkeeper give 25% discount on it . What is the sale price of the book ?
(a) : Rs (c) : Rs 25
(b0 : Rs (d) : Rs 75

83. (a) : 10% (c) : 25% (b) : 20% (d) : 40%
Q.3 : A toy marked at Rs 40 is available for Rs 32 . What % discount is given on the marked price ?
(a) : 10% (c) : 25%
(b) : 20% (d) : 40%
Q.4 : Meenu purchased a fridge for Rs 10,000 and sold it for Rs 8,000 . Find her loss .
(a) Rs 8, (c) : Rs 2,000
(b) : Rs 10, (d) : Rs 12,000

84. (a) : Rs 1,000 (c) : Rs 200 (b) : Rs 1,200 (d) : Rs 800
Q.5 : Saroj purchased a watch for Rs 1,000 and she sold it for Rs 1,200 . What is her profit ?
(a) : Rs 1, (c) : Rs 200
(b) : Rs 1, (d) : Rs 800
Q.6 : Kanti purchased a sewing machine for Rs 2,000 . She sold it at a loss of 40% . Find the selling price .
(a) : Rs 1, (c) : Rs 800
( b) : Rs (d) : Rs 2,800

85. Q. 7 : Rani purchased a T. V for Rs 10,000 and sold it for Rs 8,000
Q.7 : Rani purchased a T.V for Rs 10,000 and sold it for Rs 8,000 . Find her loss % . (a) : 10% (c) : 40% (b) : 20% (d) : 60% Q.8 : Sapna purchased a cycle for Rs 1,000 and sold it for Rs 1,200 . Find her gain %. (a) : 20% (c) : 40% (b) : 10% (d) : 12%

86. Q.9 : Find the simple interest on Rs 1,000 for 2 years at 8% per annum . (a) : Rs 80 (c) : Rs 120 (b) : Rs 40 (d) : Rs 160 Q.10 : A sofa set was brought for rs 10,000. Its value depreciated at the rate of 10% per annum. Find its value after one year . (a) : Rs 11,000 (c) : Rs 10,000 (b) : Rs 9,000 (d) : Rs 1,000

87. Q. 11 : There are 1,275 trees in Chaudary Farm
Q.11 : There are 1,275 trees in Chaudary Farm. Out of these 36% trees are of fruits. How many trees of fruits are there in Chaudary Farm ? (a) : 459 (c) : 549 (b) : 945 (d) : 954 Q.12 : The salary of Manish is Rs 10,000. His salary gets increased by 10% . Find his increased salary . (a) : Rs 9,000 (c) : Rs 8,000 (b) : Rs 11,000 (d) : Rs 12,000

88. Q. 13 : The simple interest 0n Rs 2,000 for 4 years is Rs 400
Q.13 : The simple interest 0n Rs 2,000 for 4 years is Rs The rate % of interest is : (a) : 2,000 x 100/400 x 4 (b) : 400 x 4/2,000 x 100 (c) : 400 x 100/2,000 x 4 (d) : 2,000 x 4/400 x 100

89. Q. 14 : a sum is taken for one year at 9% p. a
Q.14 : a sum is taken for one year at 9% p.a. If interest is compounded after every three months, how many times will interest charged in one year ? (a) : 2 times (c) : 4 times (b) : 3 times (d) : 1 time Answers are in the next slide :

90. Solutions :
(1) : 40 % (8) : 20% (2) : Rs 75 (9) : Rs 160 (3) : 20% (10) : Rs 9,000 (4) : Rs 2,000 (11) : 459 (5) : Rs 200 (12) : Rs 11,000 (6) : Rs 1,200 (13) : 400 x 100/2,000 x 4 (7) : 20% (14) : 4 times

91. BY :-
K . SRAVANI
VIII – B