Find the missing number in the given series

1) 

a) 91     b) 85    c) 80    d) 90

 2) 

a) 43     b) 61    c) 81    d) 31

3) 

a) 91     b) 85    c) 57    d) 90

4) 

a) 91     b) 85    c) 57    d) 70

5) 

a) 92     b) 22    c) 60    d) 42

6) 

a) 53     b) 85    c) 71    d) 97

7) 

a) 53     b) 71    c) 85    d) 97

8) 

a) 81     b) 85    c) 71    d) 87

9) 

a) 53     b) 73    c) 71    d) 97

10) 

a) 53     b) 48    c) 58    d) 56

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Answers with a small hint:-

1) a) Hint:- There is difference of 5 between two successive numbers. This is a descending order series.

2) b) Hint:- There is difference of 7 between two successive numbers. This is a descending order series.

3) c) Hint:- There is difference of 9 between two successive numbers. This is a descending order series.

4) d) Hint:- There is difference of 7 between two successive numbers. This is a descending order series.

5) d) Hint:- There is difference of 4 between two successive numbers. This is a descending order series.

6) c) Hint:- There is difference of 6 between two successive numbers. This is a descending order series.

7) b) Hint:- There is difference of 3 between two successive numbers. This is a descending order series.

8) a) Hint:- There is difference of 8 between two successive numbers. This is a descending order series.

9) b) Hint:- There is difference of 9 between two successive numbers. This is a descending order series.

10) c) Hint:- There is difference of 6 between two successive numbers. This is a descending order series.

Find the wrong number in the series

1) 6203, 6208, 6210, 6233, 6253, 6278, 6308, 6343, 6383, 6428, 6478

2) 2008, 2013, 2023, 2038, 2058, 2080, 2113, 2148, 2188, 2233, 2283

3) 833, 838, 848, 863, 883, 908, 938, 970, 1013, 1058, 1108

4) 603, 608, 618, 633, 653, 678, 708, 743, 783, 827, 878

5) 542, 547, 557, 572, 592, 619, 647, 682, 722, 767, 817

6) 422, 427, 437, 452, 473, 497, 527, 562, 602, 647, 697

7) 41, 46, 56, 71, 91, 116, 146, 180, 221, 266, 316

8) 988, 993, 1003, 1018, 1037, 1063, 1093, 1128, 1168, 1213, 1263

9) 322, 327, 337, 352, 362, 397, 427, 462, 502, 547, 597

10) 144, 149, 159, 174, 194, 219, 239, 284, 324, 369, 419

11) 9371, 9376, 9386, 9411, 9421, 9446, 9476, 9511, 9551, 9596, 9646

12) 18, 23, 33, 48, 68, 93, 122, 158, 198, 243, 293

13) 663, 666, 678, 693, 713, 738, 768, 803, 843, 888, 938

14) 1749, 1754, 1764, 1769, 1799, 1824, 1854, 1889, 1929, 1974, 2024

15) 398, 403, 413, 428, 448, 473, 503, 538, 578, 613, 673

16) 212, 217, 227, 232, 262, 287, 317, 352, 392, 437, 487

17) 948, 953, 963, 978, 998, 1023, 1053, 1088, 1127, 1173, 1223

18) 59, 64, 74, 89, 109, 134, 164, 198, 239, 284, 334

19) 327, 332, 342, 357, 377, 401, 432, 467, 507, 552, 602

20) 4, 9, 19, 34, 54, 78, 109, 144, 184, 229, 279

21) 96, 100, 111, 126, 146, 171, 201, 236, 276, 321, 371

22) 254, 259, 269, 284, 304, 329, 349, 394, 434, 479, 529

23) 458, 463, 473, 488, 508, 533, 563, 598, 638, 683, 732

24) 823, 828, 838, 853, 863, 898, 928, 963, 1003, 1048, 1098

25) 3853, 3858, 3867, 3883, 3903, 3928, 3958, 3993, 4033, 4078, 4128

26) 7122, 7127, 7137, 7152, 7172, 7187, 7227, 7262, 7302, 7347, 7397

27) 5228, 5233, 5243, 5258, 5278, 5303, 5323, 5368, 5408, 5453, 5503

28) 914, 919, 929, 944, 964, 989, 1011, 1054, 1094, 1139, 1189

29) 547, 552, 562, 577, 597, 622, 642, 687, 727, 772, 822

30) 388, 391, 403, 418, 438, 463, 493, 528, 568, 613, 663

31) 135, 142, 152, 167, 187, 212, 242, 277, 317, 362, 412

32) 9, 14, 24, 38, 59, 84, 114, 149, 189, 234, 284

33) 152, 158, 167, 182, 202, 227, 257, 292, 332, 377, 427

34) 94, 99, 109, 124, 144, 169, 199, 234, 275, 319, 369

35) 81, 86, 96, 111, 131, 156, 176, 221, 261, 306, 356

36) 201, 206, 216, 231, 251, 276, 316, 341, 381, 426, 476

37) 591, 596, 616, 621, 641, 666, 696, 731, 771, 816, 866

38) 2044, 2050, 2060, 2075, 2095, 2120, 2150, 2185, 2225, 2270, 2320

39) 4511, 4516, 4526, 4541, 4561, 4586, 4616, 4651, 4691, 4636, 4786

40) 992, 997, 1007, 1022, 1042, 1066, 1097, 1132, 1172, 1217, 1267

41) 446, 451, 461, 476, 496, 520, 551, 586, 626, 671, 721

42) 242, 247, 257, 272, 292, 307, 347, 382, 422, 467, 517

43) 34, 39, 49, 64, 84, 109, 139, 174, 214, 259, 307

44) 5, 11, 21, 36, 56, 81, 111, 146, 186, 231, 281

45) 73, 77, 88, 103, 123, 148, 178, 213, 253, 298, 348

46) 76, 81, 91, 106, 126, 151, 181, 206, 256, 301, 351

47) 746, 751, 761, 776, 796, 821, 851, 885, 926, 971, 1021

48) 4246, 4251, 4261, 4276, 4296, 4321, 4351, 4385, 4426, 4471, 4521

49) 334, 339, 349, 364, 374, 409, 439, 474, 514, 559, 609

50) 74, 79, 89, 104, 114, 149, 179, 214, 254, 299, 349

51) 29, 34, 44, 59, 69, 104, 134, 169, 209, 254, 304

52) 521, 526, 536, 551, 571, 595, 626, 661, 701, 746, 796

53) 4212, 4217, 4227, 4242, 4262, 4287, 4317, 4352, 4392, 4436, 4487

54) 249, 254, 264, 279, 300, 324, 354, 389, 429, 474, 524

55) 8, 13, 23, 38, 58, 82, 113, 148, 188, 233, 283

56) 582, 587, 597, 612, 632, 657, 687, 722, 761, 807, 857

57) 3488, 3493, 3503, 3518, 3538, 3563, 3593, 3628, 3658, 3713, 3763

58) 159, 164, 174, 189, 219, 234, 264, 299, 339, 384, 434

59) 7, 12, 22, 37, 57, 82, 112, 147, 187, 232, 281

60) 11, 16, 26, 41, 61, 86, 116, 151, 190, 236, 286

61) 82, 87, 97, 112, 132, 157, 177, 222, 262, 307, 357

62) 182, 187, 197, 212, 232, 257, 287, 320, 362, 407, 457

63) 349, 354, 374, 379, 399, 424, 454, 489, 529, 574, 624

64) 579, 584, 594, 609, 629, 654, 674, 719, 759, 804, 854

65) 906, 911, 921, 936, 956, 981, 1001, 1046, 1086, 1131, 1181

66) 3003, 3008, 3018, 3033, 3053, 3078, 3108, 3143, 3183, 3228, 3277

67) 23, 28, 38, 53, 73, 98, 128, 162, 203, 248, 298

68) 39, 44, 54, 69, 89, 114, 144, 178, 219, 264, 314

69) 208, 214, 224, 239, 259, 284, 314, 349, 389, 434, 484

70) 253, 258, 268, 283, 313, 328, 358, 393, 433, 478, 528

71) 697, 702, 712, 727, 747, 772, 812, 837, 877, 922, 972

72) 702, 707, 717, 732, 752, 767, 807, 842, 882, 927, 977

73) 999, 1004, 1014, 1029, 1049, 1074, 1114, 1139, 1179, 1224, 1274

74) 2016, 2021, 2031, 2046, 2066, 2091, 2120, 2156, 2196, 2241, 2291

75) 89, 94, 104, 109, 139, 164, 194, 229, 269, 314, 364

76) 278, 283, 293, 308, 328, 353, 382, 418, 458, 503, 553

77) 554, 559, 569, 584, 614, 629, 659, 694, 734, 779, 829

78) 903, 908, 918, 933, 953, 978, 998, 1043, 1083, 1128, 1178

79) 54, 59, 69, 84, 104, 129, 159, 194, 214, 279, 329

80) 198, 203, 213, 228, 248, 273, 302, 338, 378, 423, 473

81) 507, 512, 522, 537, 555, 582, 612, 647, 687, 732, 782

82) 921, 926, 936, 951, 971, 995, 1026, 1061, 1101, 1146, 1196

83) 66, 71, 81, 96, 117, 141, 171, 206, 246, 291, 341

84) 123, 128, 139, 153, 173, 198, 228, 263, 303, 348, 398

85) 777, 783, 793, 808, 828, 853, 883, 918, 958, 1003, 1053

86) 989, 994, 1003, 1019, 1039, 1064, 1094, 1129, 1169, 1214, 1264

87) 390, 395, 405, 420, 440, 465, 495, 530, 570, 614, 665

88) 494, 499, 509, 524, 544, 569, 599, 634, 678, 719, 769

89) 113, 118, 128, 143, 165, 188, 218, 253, 293, 338, 388

90) 876, 881, 891, 906, 926, 955, 981, 1016, 1056, 1101, 1151

=================================================

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Answers : - 1) 6210, 2) 2080, 3) 970, 4) 827, 5) 619, 6) 473, 7) 180, 8) 1037, 9) 362, 10) 239, 11) 9411, 12) 122, 13) 666, 14) 1769, 15) 613, 16) 232, 17) 1127, 18) 198, 19) 401, 20) 78, 21) 100, 22) 349, 23) 732, 24) 863, 25) 3867, 26) 7187, 27) 5323, 28) 1011, 29) 642, 30) 391, 31) 135, 32) 38, 33) 158, 34) 275, 35) 176, 36) 316, 37) 616, 38) 2044, 39) 4636, 40) 1066, 41)520, 42) 307, 43) 307, 44) 5, 45) 77, 46) 206, 47) 885, 48) 4385, 49) 374, 50) 114, 51) 69, 52) 595, 53) 4436, 54) 300, 55) 82, 56) 761, 57) 3658, 58) 219, 59) 281, 60) 190, 61) 177, 62) 320, 63) 374, 64) 674, 65) 1001, 66) 3277, 67) 162, 68) 178, 69) 208, 70) 313, 71) 812, 72) 767, 73) 1114, 74) 2120, 75) 109, 76) 382, 77) 614, 78) 998, 79) 214, 80) 302, 81) 555, 82) 995, 83) 117, 84) 139, 85) 777, 86) 1003, 87) 614, 88) 678, 89) 165, 90) 955

Find the wrong number in the series

1) Which is the wrong number in the given series:- 16, 21, 31, 46, 66, 90, 121, 156

(a) 90                     (b) 121                  (c) 66                     (d) 31

Answer: (a) 90

Solution with explanation:-

Every series has its own rule. Let us find the rule of this series.

Let a=16, b=21, c=31, d=46, e=66, f=90, g=121 and h=156 are numbers in series.

So b = 21 = 16 + 5

c = 31 = 21 + 10

d = 46 = 31 + 15

e = 66 = 46 + 20 and so on.

Thus we have to add respective multiple of 5 to get the next number.

Thus the number on 6^th position that is

f = 66 + 25 = 91.

And number on 7^th position means

g = 91 + 30 = 121.

g = 121 is given correctly in the series but given number f = 90 is wrong. Hence the wrong number in the series is 90 in the option (a).

Now practice the following problems based on the same series rule that is adding multiple of 5 to get next number.

2. Find out the wrong number in the following series:-

1) 3, 8, 18, 30, 53, 78, 108, 143, 183, 228, 278

(a) 18                     (b) 30                    (c) 143                   (d) 278

2) 62, 67, 77, 92, 110, 137, 167, 202, 242, 287, 337

(a) 287                  (b) 202                  (c) 110                   (d) 337

3) 163, 169, 178, 193, 213, 238, 268, 303, 343, 388, 438

(a) 303                  (b) 193                  (c) 438                   (d) 169

4) 282, 287, 297, 312, 332, 350,    387, 422, 462, 507, 557

(a) 422                  (b) 312                  (c) 350                   (d) 282

5) 549, 554, 564, 579, 599, 624, 650, 689, 729, 774, 824

(a) 18                     (b) 30                    (c) 143                   (d) 650

6) 783, 788, 798, 813, 833, 858, 888, 920, 963, 1008, 1058

(a) 783                  (b) 920                  (c) 888                   (d) 1008

7) 937, 942, 952, 967, 987, 1012, 1042, 1077, 1110, 1162, 1212

(a) 1110        (b) 942            (c) 942           (d) 987

8) 1309, 1314, 1320, 1339, 1359, 1384, 1414, 1449, 1489, 1534, 1584

(a) 1320                (b) 1584                (c) 1384             (d) 1414

9) 3599, 3604, 3614, 3629, 3649, 3674, 3700, 3739, 3779, 3824, 3874

(a) 3604                (b) 3629                (c) 3700            (d) 3874

10) 9933, 9938, 9948, 9963, 9983, 10007, 10038, 10073, 10113, 10158, 10208

(a) 10073              (b) 10007               (c) 9963            (d) 9948

Answers: - 1) = (b), 2) = (C), 3) = (d), 4) = (c), 5) = (d), 6) = (b), 7) = (a), 8) = (a), 9) = (c), 10) = (b)

=================================================

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1) 6210, 2) 2080, 3) 970, 4) 827, 5) 619, 6) 473, 7) 180, 8) 1037, 9) 362, 10) 239, 11) 9411, 12) 122, 13) 666, 14) 1769, 15) 613, 16) 232, 17) 1127, 18) 198, 19) 401, 20) 78, 21) 100, 22) 349, 23) 732, 24) 863, 25) 3867, 26) 7187, 27) 5323, 28) 1011, 29) 642, 30) 391, 31) 135, 32) 38, 33) 158, 34) 275, 35) 176, 36) 316, 37) 616, 38) 2044, 39) 4636, 40) 1066, 41)520, 42) 307, 43) 307, 44) 5, 45) 77, 46) 206, 47) 885, 48) 4385, 49) 374, 50) 114, 51) 69, 52) 595, 53) 4436, 54) 300, 55) 82, 56) 761, 57) 3658, 58) 219, 59) 281, 60) 190, 61) 177, 62) 320, 63) 374, 64) 674, 65) 1001, 66) 3277, 67) 162, 68) 178, 69) 208, 70) 313, 71) 812, 72) 767, 73) 1114, 74) 2120, 75) 109, 76) 382, 77) 614, 78) 998, 79) 214, 80) 302, 81) 555, 82) 995, 83) 117, 84) 139, 85) 777, 86) 1003, 87) 614, 88) 678, 89) 165, 90) 955

Numerical: Area of circle

1) The inner circumference of a 21m wide circular race track is 660m. Then

(A) What is radius of inner edge circle of race track?

(B) What is radius of outer edge circle of race track?

(C) What is perimeter of outer edge circle of race track?

(D) What is area of inner edge circle of race track?

(E) What is area of outer edge circle of race track?

(F) What is area of circular race track?

(G) How much long rope will be required to tie all the poles around both sides of the               race tack?

Options for question (A) : (a) 84 m. (b) 105 m. (c) 100 m. (d) 66 m.

Options for question (B) : (a) 84 m. (b) 105 m. (c) 126 m. (d) 66 m.

Options for question (C) : (a) 729 m. (b) 512 m. (c) 1000 m. (d) 880 m.

Options for question (D) : (a) 84125 sq.m. (b) 10025 sq.m. (c) 78250 sq.m. (d) 34650 sq.m.

Options for question (E) : (a) 49896 sq.m. (b) 10025 sq.m. (c) 78250 sq.m. (d) 34650 sq.m.

Options for question (F) : (a) 84125 sq.m. (b) 15246 sq.m. (c) 78250 sq.m. (d) 34650 sq.m.

Options for question (G) : (a) 1415 m. (b) 1052 m. (c) 1389 m. (d) 1766 m.

Answers with explanation:

Equations used to solve this problem are:

Equation of perimeter of a circle = 2πr

Equation of area of circle = πr²

(a²– b²) = (a+b)(a-b) in the form (R² – r²) = (R+r)(R-r)

Assumptions:

Let the radius of inner circle= r

Radius of outer circle = R

Given data:

Perimeter of inner edge circle of race track = 660m

Width of the race track = 21m

Let us find out radius of inner circle that is answer of question (A).

2πr = 660m.

We know that π = 22/7

So 2 X 22/7 X r = 660

Therefore, r = (660 X 7)/(2 X 22)  = 15 X 7 = 105 m

Hence r = 105 m.

Thus the radius of inner edge circle of race track is 105m.

Now radius of outer circle will be easy to find. It will be the answer of (B).

As per given data and assumptions R = r + 21 = 105 + 21 = 126 m.

Hence R = 126 m.

Thus the radius of outer edge circle of race track is 126m.

Let us find out perimeter of outer circle means answer of question (C)

Perimeter of a circle = 2πR = 2 X 22/7 X 126 = 729m.

Hence the perimeter of the outer edge circle of the race track is 729m.

The answer of questions (D) and (E) will be easy to find as we know the radii of both the circles.

The area of inner circle = πr² =  22/7 X 105² = 34650 sq. m.

Thus the area of inner edge circle of the race track is 34650 sq. m.

The area of outer circle = πR² =  22/7 X 126² = 49896 sq. m.

Thus the area of outer edge circle of race track is 49896 sq. m.

As we know the areas of both circles it is very easy to find out the area of the race track that is the answer of question (F).

Area of race track = area of outer edge circle – area of inner edge circle

                                    = 49896 – 34650 = 15246 sq. m.

There is another way to find out the area of race track by using the 3^rdequation as follows:

Area of race track = area of outer edge circle – area of inner edge circle

Area of race track = πR² - πr² = π(R² – r²) = π(R+r)(R-r)

Area of race track = 22/7 (126 + 105)(126 – 105) = 22/7 X 231 X 21 = 22 X 231 X 3

Area of race track = 15246 sq. m.

Thus the area of the race track is 15246 sq. m.

Now it’s turn of last question (G).

The required length of rope will be equal to the perimeters of both the circles.

So Length of the rope = perimeter of outer circle + perimeter of inner circle.

Length of the rope = 729 + 660 = 1389m.

Thus the length of the rope required to tie all the poles around both sides of the race track is 1389m.

Thus you can solve the numericals of this type by using the same way I solved this.

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Practice: Area of circle

In this article you will have sums on the area of two concentric circles. These are for your guidance and hence a note to solve each numerical is also given in this article. Keep solving and practicing.

1) The perimeter of inner edge of a hollow circular disk is 11cm and the disk is 7cm wide then what is the perimeter of the outer edge of the disk?

(a) 55cm         (b) 50cm         (c) 32cm         (d) none of these

Answer:- 1) = (a) 55cm,

Note: Find the inner radius and outer radius

2) A hollow bamboo is having circular shape with its inner perimeter 99mm with a thickness of 7mm, then what will be length of rope which ties it with other bamboo?

(a) 155mm      (b) 143mm      (c) 132mm      (d) 164mm

Answer: - 2) = (b) 143mm,

Note: - Find outer perimeter

3) Renuka was having a circular stamp to draw smiley face. The inner perimeter of the inner circle was 22mm and its thickness was 7mm, then what was the coloured area of the stamp?

(a) 220sq. mm                        (b) 700 sq. mm           (c) 308 sq. mm           (d) 207 sq. mm

Answer: - 3) (c) 308 sq. mm,

Note: Find area of both the circles and subtract area of inner circle from outer circle.

4) There were many circular discs made of wood with a thickness of 7cm and inner radius of 5.25cm. Then the width of the paper used to cover inner rod and outer box to hold the discs in one column before cutting?

(a) 120cm       (b) 55cm         (c) 110cm       (d) 130cm

Answer: - 4) = (c) 110cm

Note: - Find perimeters of both circles

5) A circular sitting bench is having inner diameter of 88cm and it is 70cm wide then what will be the area occupied by the bench?

(a) 18000 sq. cm         (b) 16340 sq. cm         (c) 18634 sq. cm         (d) can’t say

Answer: - (c) 18634 sq. cm

Note: - The area of outer circle

6) A toy train is having circular track with inner perimeter of 55 cm. And the width of the toy train track is 7 cm. To decorate this toy train on the occasion of a party a glittery less was pasted in both the sides of the tracks. Then what is the length of the less used for decoration?

(a) 154 cm      (b) 110 cm      (c) 77 cm        (d) 169 cm

Note: - Find the perimeter of outer circle and add both perimeters.

Answer: - (a) 154 cm

7) A circular tent is having an inner circular play area of diameter 21m. And the width of sitting area is 7m. Then what is the diameter of the tent.

(a) 28m           (b) 70m           (c) 35m           (d) 42m

Note: - Inner diameter + 2(width of sitting area)

Answer: - (c) 35m

8) A circular stadium is having an open space of perimeter 77m and running track of 7m. Then what is the length of the first sitting line of the stadium right near to running track?

(a) 225m         (b) 350m         (c) 121m         (d) can’t say

Note: - Find the perimeter of outer circle of the running track.

Answer: - (c) 121m

9) A 7mm thick bangle is having inner perimeter of 88mm. Then what is the area of the inner circle drawn using the bangle?

(a) 616 sq.mm                        (b) 660 sq.mm                        (c) 788 sq.mm                        (d) 477 sq.mm

Note: - Find radius of inner circle and then area of the inner circle.

Answer: - (a) 616 sq.mm

10) A circular stadium is having a ground of 1.75m radius and sitting area of length 14m. Then what is the area of the sitting area of the stadium?

(a) 220sq.m     (b) 770sq.m     (c) 175sq.m     (d) 1000sq.m

Note: - Find area of both the circles and then subtract area of inner circle from area of outer circle.

Answer: - (b) 770sq.m

=================================================

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=====================================================

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