Quant Quiz

Q.1 A and B working together can complete a piece of work in 12 days, while B and C can complete the same work in 16 days. A and B started working together but after 5 days A was replaced by C; after 5 more days B left the work. The remaining work was then completed by C in 13 days. In how many days would C alone be able to complete the whole work?

1. 16 days
2. 24 days
3. 32 days
4. 36 days
5. 48 days

Q.2 The ratio of investments by 2 partners Prince and Deepak is 5 : 6 and the ratio of their profits is 4 : 3. If Deepak invested his money for 10 months, then for how many months did Prince invest his money?

1. 12
2. 10
3. 9
4. 8
5. 16

Q.3 Ram invested Rs. 7,000 at the rate of 20% per annum and Rs. 8,000 at the rate of 26% per annum. What is the ratio of the respective amounts received by each of them at the end of one year?

1. 5 : 6
2. 6 : 5
3. 4 : 5
4. 5 : 4
5. None of these

Q.4 In two alloys, aluminium and iron are in the ratio of 4 : 1 and 1 : 3. After mixing together 10 kg of the first alloy, 16 kg of the second and several kilograms of pure aluminium, an alloy was obtained in which the ratio of aluminium to iron was 3 : 2. Find the weight of the new alloy.

1. 15 kg
2. 25 kg
3. 65 kg
4. 95 kg
5. 35 kg

Q.5 A shopkeeper purchased 6 kg rice at Rs. 12 per kg and mixed it with 2 kg white grains at Rs. 14 per kg. The mixture needs to be grinded before selling. Grinding of the mixture cost 20 paise per kg. At what price (in Rs. per kg) should the shopkeeper sell the mixture so as to gain 20% on the whole transaction?

1. Rs. 14.25
2. Rs. 13.20
3. Rs. 14.72
4. Rs. 15.24
5. None of these

Directions (Q.6 to 10): In each of the given questions, find the wrong term in the series.

Q.6) 13, 40, 121, 364, 1072, 3280

1. 13
2. 40
3. 364
4. 1072
5. 3280

Q.7) 4, 23, 60, 121, 212, 338

1. 23
2. 121
3. 212
4. 338
5. 4

Q.8) 97, 77, 60, 45, 32, 21

1. 97
2. 77
3. 60
4. 45
5. 32

Q.9) 157, 126, 97, 74, 57, 38

1. 157
2. 126
3. 97
4. 74
5. 57

Q.10) 56, 38, 83, 57, 112, 76

1. 56
2. 38
3. 83
4. 57
5. 112

Answers:

Q1-5

48 days
Work done by A and B together in one day = 1/12
Work done by B and C together in one day = 1/16
A and B worked for 5 days, B and C worked together for 5 days and C worked alone for 13 days.
So, part of work completed by all is
5(1/12) + 5(1/16) + 13C = 1
—-> C = 1/48
—-> C will take 48 days to complete the work.

Q2-5

16 months
The amount of profit given at the end of the period is proportional to the product of the capital invested and the number of months i.e
4/3 = 5/6* t/10
—> T = 4/3*6/5*10
—> T = 16 months

Q3-1

5 : 6
Amounts received after one year:
Amount at 20% = 7000 (1 + 20/100) = 8400
Amount at 26% = 8000 (1 + 26/100) = 10080
Required ratio = 8400/10080 = 5/6 or 5:6

Q4-5

35 kg
Quantity of aluminum in first alloy = 4/5 * 10 = 8 kg
Quantity of aluminium in second alloy = ¼ * 16 = 4 kg
Let x kg of pure aluminium be mixed.
So, 8+ 4 + x = 3/5 (10 + 16 +x)
60 + 5x = 78 +3x
2x = 18
X = 9 kg.
So,  the weight of the new alloy = 10 + 16 + 9 = 35 kg.

Q5-4

Rs. 15.24
Total cost = 6 * 12 + 2 * 14 + (6+2) (0.2) 
= 101.60
Total selling price = 101.60 * 1.2 = 121.92
So, selling price per kg = 121.92/8 = 15.24
Rs. 15.24

Q6- 4

1072
The series is moving as:
13 × 3 + 1 = 40
40 × 3 + 1 = 121
121 × 3 + 1 = 364
364 × 3 + 1 = 1093 (1072)
1093 × 3 + 1 = 3280
Hence, the wrong term of the series is 1072.

Q7-4

338
The series is moving as:
2³ – 4 = 4
3³ – 4 = 23
4³ – 4 = 60
5³ – 4 = 121
6³ – 4 = 212
7³ – 4 = 339 (338)
Hence, the wrong term of the series is 338.

Q8- 1

97
The series is moving as:
10 × 9 + 6 = 96 (97)
9 × 8 + 5 = 77
8 × 7 + 4 = 60
7 × 6 + 3 = 45
6 × 5 + 2 = 32
5 × 4 + 1 = 21
Hence, the wrong term is 97.

Q 9-5

57
The series is moving as:
157 – 31 = 126
126 – 29 = 97
97 – 23 = 74
74 – 19 = 55 (57)
55 – 17 = 38
Hence, the wrong term in the series is 57

Q 10- 3

83

There are two alternate series moving as 56, 84, 112 and 38, 57, 76. The common difference of the two series is 28 and 19 respectively.

Hence, the wrong term of the series is 83.