Syllabus- Quantitative Aptitude – Number Sequences, Series, Averages, Number Systems, Ratio and Proportion, Profit and Loss.
Prelims: 15
prelims Questions of the day-
1.The 8th term of an AP is 17 and the 19th term is 39. Find the 20th term.
- 42
- 41
- 45
- 67
Answer: B
Explanation:
T8 = a + 7d =17 …(i)
T19 = a + 18d = 39 … (ii)
On subtracting Eq. (i) from Eq. (ii), we get 11d = 22 => d = 2
Putting d = 2 in Eq. (i), we get a + 7(2) = 17 = a = (17 – 14) = 3
First term = 3, Common difference = 2
T20 = a + 19d = 3 + 19(2) = 41
2.Average weight of 32 students of a class is 30.5 kg. If weight of a teacher is also included, then average weight is increased by 500 g. What is the weight of the teacher?
- 57
- 89
- 47
- 63
Answer: C
Explanation:
Total weight of 32 students = 30.5 × 32 = 976 kg
Average weight of (32 students + 1 teacher) = (30.5 + 0.5) = 31 kg
Total weight of (32 students + 1 teacher) = 31 × 33 = 1023 kg
Weight of teacher = (1023 – 976) kg = 47 kg
3.Vaibhav started a business with an investment of Rs. 42,000. After 5 months Amit joined him with a capital of Rs. 22,000. At the end of the year the total profit was Rs. 16,409. What is Vaibhav’s share in the profit?
- Rs. 16244
- Rs. 12568
- Rs. 10782
- Rs. 5677
Answer: B
Explanation:
Ratio of the equivalent capitals of Vaibhav and Amit for 1 year = 42000 × 12 : 22000 × 7
= 42 × 12 : 22 × 7 = 252 : 77
Total profit = Rs. 16409
| Vaibhav share = Rs. | 252 | × 16409 = Rs.12568 |
| 252 + 77 |
Hence, option (B) is correct.
4.The first term of an AP is -1 and the common difference is -3, then find the 12th term is?
- -33
- -34
- -46
- -54
Answer: B
Explanation:
T1 = a = –1, d = –3
Tn = a + (n – 1)d
Tn=–1 + (n – 1) (–3)
Tn = 2 – 3n
T12 = 2 – 3 × 12 = –34
5.Find the missing number 16, 24, 36, …., 81?
- 52
- 54
- 56
- 58
Answer: B
Explanation:
Previous number × (3/2) = Next number
6.Find three numbers in AP whose sum is 36 and product is 1620.
- 9,12,15
- 3,6,9
- 5,7,9
- 12,15,18
Answer: A
Explanation:
Let the numbers be (a – d), a, (a + d).
Then, (a – d) + a + (a + d) = 36
3a = 36
a = 12
(a – d) × a × (a + d) = 1620
(12 – d) × l2 × (12 + d) = 1620
(144 – d2) – 135
d2 – 9 + d = ±3
Numbers are 9, 12, 15 or 15, 12, 9.
7.The average of five consecutive even numbers is 50. What is the largest of these numbers?
55
53
50
54
Answer: D
Explanation:
Let the numbers be x – 4, x – 2, x, x + 2, x + 4.
Average = Sum of the quantities/Number of the quantities
= (x-4+ x-2+ x+x+2+ x+4)/5 = 50
5x/5=50
x=50
So, the numbers are 46, 48, 50, 52, 54.
The largest of these numbers is 54.
8.A bag contains 50 p, 25 P and 10 p coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of 10p?
- 150
- 200
- 100
- 160
Answer: C
Explanation :
Let the number of 50 p, 25 P and 10 p coins be 5x, 9x and 4x respectively.
(5x/2)+( 9x/ 4)+(4x/10)=206
50x + 45x + 8x = 4120
1O3x = 4120
x=40.
Number of 50 p coins = (5 x 40) = 200;
Number of 25 p coins = (9 x 40) = 360;
Number of 10 p coins = (4 x 40) = 160.
9.The average salary per head of all the employees of an institution is Rs60. The average salary per head of 12 officers is Rs400 and average salary per head of the rest is Rs56. Find the total number of employees in the institution?
- 1000
- 1032
- 1024
- 932
Answer: B
Explanation: Let the total number of employees be x.
60 = Total salary of all employees/x
60 = {12 × 400 (x-12) × 56}/x
60x = 12 × 400 + (x – 12) × 56 = 4800 + 56x – 672
60x – 56x = 4800 – 672
4x = 4128
x = 1032
Hence, the total number of employees is 1032.
10.Suppose a shopkeeper has bought 1 kg of apples for Rs.100. And sold it for Rs.120 per kg. How much is the profit percentage gained by the shopkeeper?
- 25
- 40
- 50
- 20
Answer: D
Solution:
We know, Profit percentage = (Profit /Cost Price) x 100
Therefore, Profit percentage = (20/100) x 100 = 20%.
11.A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture
- 16
- 45
- 10
- 30
Answer: C
Explanation :
Let the quantity of alcohol and water be 4x litres and 3x litres respectively 4x/(3x+5) =4/5
20x=4(3x+5)
8x=20
x=2.5
Quantity of alcohol = (4 x 2.5) litres = 10 litres.
12.A man buys a fan for Rs. 1000 and sells it at a loss of 15%. What is the selling price of the fan?
- 900
- 950
- 850
- 700
Answer: C
Solution:
Cost Price of the fan is Rs.1000
Loss percentage is 15%
Loss percentage = (Loss/Cost Price) x 100
15 = (Loss/1000) x 100
Therefore, Loss = Rs.150.
Loss = Cost Price – Selling Price
So, Selling Price = Cost Price – Loss
= 1000 – 150
Selling Price = R.850/-
13.A shopkeeper gives a discount of 10% in every 4 months at an article. If a man purchases it for Rs. 25515 in the month of December, then what was the initial price of that article in the month of January?
- Rs. 40000
- Rs. 36000
- Rs. 35000
- Rs. 45000
Answer: C
Explanation:
Let the cost of article in January was Rs. x
| In the month of April, the cost of the article = Rs. | 90 x |
| 100 |
In the month of August, the cost of that article
| = | 90x | × | 90 | = Rs. | 81x |
| 100 | 100 | 100 |
In the month of December, the cost of that article
| = | 81x | × | 90 | = Rs. | 729x |
| 100 | 100 | 1000 |
| Given, | 729x | = 25515 |
| 1000 |
X = Rs.35000
Hence, option (C) is correct.
14.Find the missing number in the series 5040, 720, 120, 24, ….2,1?
- 8
- 7
- 6
- 5
Answer: C
Explanation:
5040/7=720
720/6=120
120/5=24
24/4=6
6/3=2
2/2=1
15.In a class with a certain number of students if one new student weighing 50 kg is added, then average weight of class is increased by 1 kg. If one more student weighing 50 kg is added, then the average weight of the class increases by 1.5 kg over the original average. What is the original average weight (in kg) of the class?
- 46
- 42
- 27
- 47
Answer: D
Explanation:
Let x be the number of students in the class and y be the average weight of the class
Now according to question,
| xy + 50 | = y + 1 |
| x + 1 |
x + y = 49 ………. (i) Again,
| xy + 50 + 50 | = y + 1.5 |
| x + 2 |
1.5x + 2y = 97 ………. (ii)
From equation (i) and (ii), we get y = 47
Hence, option (D) is correct.