This set of Aptitude Questions and Answers (MCQs) focuses on “Series”.
1. 5 numbers a, b, c, d and e are in a ratio 11 : 18 : 24 : 17 : 29. A new ratio is formed with the values 20% of a, 45% of b, 80% of c, 50% of d and 40% of e. Arrange the new ratio in ascending order and select the option with the correct variable in the correct form.
a) a : b : c : d : e
b) a : b : e : d : c
c) a : b : d : e : c
d) a : c : e : d : b
View Answer
Explanation: Let the ratios be in terms of x.
20% of a = 20% of 11x = 2.2x
45% of b = 45% of 18x = 8.1x
80% of c = 80% of 24x = 19.2x
50% of d = 50% of 17x = 8.5x
40% of e = 40% of 29x = 11.6x
In ascending order, the numbers will be 2.2x : 8.1x : 8.5x : 11.6x : 19.2x = a : b : d : e : c
2. 4 numbers are in a ratio 1 : 2 : 3 : 4. The numbers are increased by 40%, 30%, 20% and 10% respectively. Find the new ratio.
a) 4 : 3 : 2 : 1
b) 1 : 2 : 3 : 4
c) 7 : 13 : 18 : 22
d) 22 : 18 : 13 : 7
View Answer
Explanation: the initial ratio = 1 : 2 : 3 : 4
The increased ratio = 1 + 40% of 1 : 2 + 30% of 2 : 3 + 20% of 3 : 4 + 10% of 4
The new ratio = 1.4 : 2.6 : 3.6 : 4.4
The new ratio = 14 : 26 : 36 : 44 = 7 : 13 : 18 : 22
3. The ratio of a series of 5 numbers is 4 : 5 : 6 : 7 : 8. Find the new ratio if each number is increased by 60%.
a) 5 : 6 : 7 : 8 : 9
b) 4 : 5 : 6 : 7 : 8
c) 3 : 4 : 5 : 6 : 7
d) 2 : 3 : 4 : 5 : 6
View Answer
Explanation: There will be no change in the series as each term is increasing with the same percentage.
The new terms of the series are :
4 + 60% of 4 = 4 + 2.4 = 6.4
5 + 60% of 5 = 5 + 3 = 8
6 + 60% of 6 = 6 + 3.6 = 9.6
7 + 60% of 7 = 7 + 4.2 = 11.2
8 + 60% of 8 = 8 + 4.8 = 12.8
The new ratio = 6.4 : 8 : 9.6 : 11.2 : 12.8 = 0.8 : 1 : 1.2 : 1.4 : 1.6 = 4 : 5 : 6 : 7 : 8 hence there is no change.
4. 6 terms if a series are in a ratio 4 : 5 : 6 : 7 : 8 : 9. If the difference between the first and the last term is 15 and each term is increased by 12, find the new ratio of the series.
a) 6 : 7 : 8 : 9 : 10 : 11
b) 7 : 8 : 9 : 10 : 11 : 12
c) 8 : 9 : 10 : 11 : 12 : 13
d) 9 : 10 : 11 : 12 : 13 : 14
View Answer
Explanation: The difference between the first and last term = 15
Let the terms be in terms of x.
9x – 4x = 5x = 15
X = 15 / 5 = 3
The terms = 4x, 5x, 6x, 7x, 8x and 9x = 12, 15, 18, 21, 24 and 27
On adding 12 to each term we get 24, 27, 30, 33, 36 and 39.
Now 24 : 27 : 30 : 33 : 36 : 39 = 8 : 9 : 10 : 11 : 12 : 13
5. There are 5 terms in a series 94, 85, 81, 80, 90. If the first two numbers are increased by 20 and the last two numbers are increased by 20%, find the ratio of the terms of the series then formed.
a) 38 : 27 : 35 : 36 : 32
b) 38 : 35 : 27 : 32 : 36
c) 39 : 35 : 32 : 39 : 34
d) 39 : 34 : 35 : 27 : 29
View Answer
Explanation: The first 2 terms of the new series = 94 + 20 and 85 + 20 = 114 and 105
The third term of the series will be unchanged = 81
The last two terms of the series will be 80 + 20% of 80 and 90 + 20% of 90 = 80 + 16 and 90 + 18 = 96 and 108.
The new series formed = 114, 105, 81, 96, 108
The ratio of the new series = 38 : 35 : 27 : 32 : 36
6. A series of 4 digits with the terms 55, 66, 77 and 88 is first arranged in descending order and increased in the following way 20%, 40%, 60% and 120%. Find the ratio of the new series formed.
a) 48 : 48 : 49 : 55
b) 49 : 49 : 48 : 55
c) 48 : 49 : 48 : 55
d) 49 : 48 : 49 : 55
View Answer
Explanation: The series in descending order = 88, 77, 66, 55
The new series = 88 + 20% of 88, 77 + 40% of 77, 66 + 60% of 66 and 55 + 120% of 55
The new series = 88 + 17.6, 77 + 30.8, 66 + 39.6 and 55 + 66
The new series = 105.6, 107.8, 105.6 and 121
The ratio = 1056 : 1078 : 1056 : 1210 = 48 : 49 : 48 : 55
7. A series of 5 terms is 23, 34, 45, 56, 67. If each term is increased by 7 and then decreased by 57% find the ratio of the series then formed.
a) 29 : 30 : 41 : 52 : 63
b) 30 : 41 : 52 : 63 : 74
c) 28 : 39 : 40 : 51 : 62
d) 33 : 44 : 55 : 66 : 77
View Answer
Explanation: It is known that if each term of the series is increased by a same percentage the ratio remains the same. The ratio of the new series will be 23 + 7 : 34 + 7 : 45 + 7 : 56 + 7 : 67 + 7 = 30 : 41 : 52 : 63 : 74
8. The first three terms of a series are increased by 50% and the last 3 terms of the series are decreased by 50%. If the series so formed is 33, 42, 48, 50, 55, 60, find the ratio of the initial series.
a) 12 : 15 : 17 : 50 : 55 : 60
b) 11 : 14 : 16 : 50 : 55 : 60
c) 10 : 13 : 15 : 50 : 55 : 60
d) 9 : 12 : 14 : 50 : 55 : 60
View Answer
Explanation: The initial terms will be :
33 / 150 * 100 = 22
42 / 150 * 100 = 28
48 / 150 * 100 = 32
50 / 50 * 100 = 100
55 / 50 * 100 = 110
60 / 50 * 100 = 120
The initial series = 22, 28, 32, 100, 110, 120
The ratio of the initial series = 11 : 14 : 16 : 50 : 55 : 60
9. There are 3 terms in a series if the first term is twice as the third term and the second term is half as of the third term, find the ratio of the series.
a) 1 : 2 : 4
b) 4 : 2 : 1
c) 1 : 4 : 2
d) 4 : 1 : 2
View Answer
Explanation: Let the third term of the series be 2x.
The first term of the series = twice the third term = 2 * 2x = 4x
The second term is half the third term = 2x / 2 = x
The required ratio = 4x : x : 2x = 4 : 1 : 2
10. There are 5 terms a, b, c, d and e in a series. A = 4b, b = 7c, c = 2d, d = half of e and e = 12. Find the ratio of the series.
a) 56 : 14 : 2 : 1 : 1
b) 56 : 2 : 14 : 1 : 2
c) 56 : 14 : 2 : 1 : 1
d) 56 : 14 : 2 : 1 : 2
View Answer
Explanation: e = 12
D = e / 2 = 12 / 2 = 6
C = 2d = 6 * 2 = 12
B = 7c = 12 * 7 = 84
A = 4b = 84 * 4 = 336
The required ratio = 336 : 84 : 12 : 6 : 12 = 56 : 14 : 2 : 1 : 2
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