Direction (1-5): The following questions contain two equations as I and II. You have to solve both the questions and determine the relationship between them and give answers as,
- A) x > y
- B) x ≥ y
- C) x < y
- D) x ≤ y
- E) x = y or the relation cannot establish.
1. Question
I) x2 – 10x – 24 = 0
II) y2 + 16y – 36 = 0
Solution:
Answer: E
x2 – 10x – 24 = 0
x2 – 12x + 2x – 24 = 0
(x – 12) (x + 2) = 0
x = 12 , – 2
y2 + 16y – 36 = 0
y2 + 18y – 2y – 36 = 0
(y + 18)( y – 2)= 0
y= 2 , -18
Thus, the relationship can not be established between x and y.
2. Question
I) x – (256)1/4 = 0
II) y2 + (125)1/3 = 21
Solution:
Answer: B
x – (256)1/4 = 0
x = (256)1/4
x = 4
y2 + (125)1/3 = 21
y2 + 5 = 21
y2 = 16
y = +4, -4
Thus, x is either greater than or equal to y.
3. Question
I) x2 – 5x -14 = 0
II) y2 + 9y + 20 = 0
Solution :-
Answer : A
x2 – 5x -14 = 0
x2 – 7x + 2x – 14 = 0
(x – 7) (x + 2) =0
x = 7, -2
y2 + 9y + 20 = 0
y2 + 5y + 4y + 20 = 0
(y + 4) (y + 5) = 0
y = -4, -5
Thus, x is greater than y.
4. Question
I) 10x2 – 3x – 1 = 0
II) y2 + 5y = – 6
Solution:
Answer : A
10x2 – 3x – 1 = 0
10x2 – 5x + 2x – 1 = 0
5x(2x – 1) + 1(2x – 1) = 0
(2x – 1) (5x + 1) = 0
x = 1/2 , -1/5
y2 + 5y + 6 = 0
y2 + 2y + 3y + 6 = 0
y(y + 2) + 3 (y + 2) = 0
(y + 2)(y + 3) = 0
y = -3 , -2
x > y
Thus, x is greater than y.
5. Question
I) x2 + 17x + 42 = 0
II) 2y2 – 15y + 22 = 0
Solution:
Answer : C
x2 + 17x + 42 = 0
x2 + 14x + 3x + 42 = 0
x(x + 14) + 3 (x + 14) = 0
(x + 14) (x + 3) = 0
x = -14 , – 3
2y2 – 15y + 22 = 0
2y2 – 11y – 4y + 22 = 0
y (2y – 11) – 2(2y – 11) = 0
(y – 2) (y – 11) = 0
y = 2, 11/2
x < y
Thus, y is greater than x.
Directions (6 -10): What number should come in the place of (?) in the following number series?
6. Question
5, 30, 150, 600, ?
a) 1500
b) 1200
c) 1300
d) 1800
e) 2000
Solution:
Answer: D
5 * 6 = 30
30 * 5 = 150
150 * 4 = 600
600 * 3 = 1800
Thus, the number is 1800.
7. Question
104, ?, 96, 120, 88, 128
a) 108
b) 112
c) 120
d) 96
e) 100
Solution:
Answer: B
104 + 8 = 112
112 – 16 = 96
96 + 24 = 120
120 – 32 = 88
88 + 40 = 128
Thus, the number is 112.
8. Question
15, 8, 9, 15, 32, ?
a) 60
b) 72
c) 82.5
d) 80
e) 96
Solution:
Answer: C
15 * 0.5 + 0.5 = 8
8 * 1 + 1 = 9
9 * 1.5 + 1.5 = 15
15 * 2 + 2 = 32
32 * 2.5 + 2.5 = 82.5
Thus, the number is 82.5
9. Question
26, 63, 124, 215, ?
a) 315
b) 325
c) 332
d) 326
e) 342
Solution:
Answer: E
63 – 26 = 37
124 – 63 = 61 (Difference b/w 61-37=24)
215 – 124 = 91 ( Difference b/w 91-60=30)
Each time +6 is added so next number is 36 .
It should be added to 91 , the sum is = ( 91 + 36) = 127
Again this 127 should be added to 215 ,
Sum is = ( 127 + 215 ) = 342
Thus, the number is 342.
10. Question
200, 197, 185, 163, ?
a) 130
b) 120
c) 150
d) 140
e) 160
Solution:
Answer : A
(200 – 197) = 3
(197 – 185 ) = 12 (Difference b/w 12 – 3 = 9)
(185 – 163 ) = 22 (Difference b/w 22 – 12 = 10)
Each time + 1 added, So the next number should be 10 + 1 = 11
It should be added to 22 ,
(22 + 11) = 33
this 33 subtracted from 163 ,
( 163 – 33) = 130
Thus, the number is 130.
11. Question
A clerk can able to typing at a certain speed. He increases his typing by 10% per hour in the first two hours, decreases by 10% in the next one hour, remains constant in the next one hour, and again increases by 5% per hour in the next two hours. If the total original typing is 40000, find the approximate word typing at the end of 6 hours.
a) 45000
b) 50000
c) 47200
d) 48025
e) 48050
Solution:
Answer: D
10% = 1/10
5% = 1/20
| |
Original
|
Now
|
| 1st hour |
10
|
11
|
| 2nd hour |
10
|
11
|
| 3rd hour |
10
|
09
|
| 5th hour |
20
|
21
|
| 6th hour |
20
|
21
|
| |
= 400000
|
= 480249 ( ≈ 480250)
|
∴ 480250 ÷ 10 = 48025
∴The word typing (approximately) at the end of 6 hours is 48025.
12. Question
Seven years ago, the age of Amit and the present age of Bala is in the ratio of 3:4. After eight years, the age of Amit and Bala will be in the ratio of 3:2. Find the present age of Bala?
a) 6 years
b) 8 years
c) 4 years
d) 7 years
e) None of these
Solution:
Answer: B
The ratio of age of Amit 7 years ago and the present age of Bala
= 3 : 4 (3x, 4x)
Present age of Amit and Bala = 3x + 7, 4x
According to the question,
(3x + 7 + 8)/(4x + 8) = (3/2)
12x + 6 = 6x + 18
x = 2
Thus, the present age of Bala is = 4x = 8 years.
13. Question
A boy is written a set of three numbers in his notebook, the average of the first two numbers is 8, the average of the last two numbers is 9 and the average of the first and last numbers is 10. Find the average of three numbers?
a) 9
b) 10
c) 11
d) 6
e) 7
Solution:
Answer: A
Let the numbers be x, y and z,
The average of first two numbers = 8
(x + y) = 16
The average of last two numbers = 9
(y + z) = 18
The average of first and last numbers = 10
(x + z) = 20
2*(x + y + z) = 16 + 18 + 20 = 54
x + y + z = 27
Required average = (27/3) = 9
Thus, the average of three numbers is = 9.
14. Question
A man is rowing a boat. He is moving a certain distance downstream with thrice speed than upstream. Find out the ratio of the speed of the boat in still water to the speed of the current.
(a) 2:1
(b) 5:1
(c) 7:1
(d) 3:1
(e) None of the above
Solution:
Answer: A
Let speed boat in still water be x km/hr
speed of current = y km/h
Speed downstream = (x + y) km/hr
Speed upstream = (x – y) km/hr
According to the question,
3(x – y) = (x + y)
2x = 4y
x : y = 2 : 1
Thus, the ratio between the speed of boat in still water and the speed of current is = 2:1
15. Question
A biker took 30 seconds less time to cross a circular ground along its diameter than to cover it along its boundary. If his speed is 36 km/hr, what is the circumference of the circle?
a) 1550 m
b) 1700 m
c) 1100 m
d) 1400 m
e) 1650 m
Solution:
Answer: e
36 km/hr × 5/18 = 10 m/s
Distance = speed × time
= 10 × 30 m
= 300 m
According to the question,
Ï€r – 2r = 15
r(22/7 – 2) = 300
r = 525/2
Circumference = 2Ï€r
= 2 × 22/7 × 525/2
=1650 m
Thus, the circumference of the circle is = 1650 m.
Direction (16-20): Read the given information carefully and answer the questions given below.
Three shopkeepers A, B & C sell burgers (veg + non-veg) in Week I. Veg & Non-veg burger sold by A are in the ratio 9:7, veg and non-veg burgers sold by B are in the ratio 3:4. Total burgers sold by C is 108, out of which veg & non-veg burgers of C are in the ratio 7:5. Total burgers sold by A, B & C together is 376. Veg burger sold by A is 20% more than the veg burger sold by B.
16. Question
Find the ratio between the veg burger sold by A and C.
a) 8: 7
b) 1: 2
c) 3: 2
d) 7: 8
e) 5: 6
Solution
Answer: A
(Explanation for 16-20)
Burger sold by C = 108
Veg burger by C = 108/12 * 7 = 63
Non- veg burger by C = 108/ 12 * 5 = 45
Burger sold by A and B = 376 – 108 = 268
Veg : Non-veg burger sold by A = 9: 7 (9y, 7y)
Veg : Non-veg burger sold by B = 3: 4 (3x, 4x)
Veg burger sold by B = 100
Veg burger sold by A = 120
Ratio = 6 : 5
9y/6 × 5 = 7.5y
7.5y/3 × 4 = 10y
A( veg ) : A( non – veg ) : B( veg ) : B( non – veg )
= 9 : 7 : 7.5 : 10
= 18: 14: 15: 20
268 = 67y
y = 4
Veg burger in A = 18 × 4 = 72
Non- veg burger in A = 14 × 4 = 56
Veg burger in B = 15 × 4 =60
Non- veg burger in B = 20 × 4 = 80
| Shopkeepers |
Total |
Veg |
Non-veg |
|
A
|
128
|
72
|
56
|
|
B
|
140
|
60
|
80
|
|
C
|
108
|
63
|
45
|
Explanation for 16 Question:
Required ratio
= 72: 63
= 8: 7
∴ The ratio of veg burger sold by A and C = 8 : 7
17. Question
Find the sum of non–veg burgers sold by all the shopkeepers.
a) 178
b) 145
c) 156
d) 175
e) 181
Solution:-
Answer: E
Required sum = 56 + 80 + 45 = 181
∴The sum of non veg burger sold by all the shopkeepers is 181.
18. Question
The veg burger sold in B is what percentage of non–veg burgers sold in B?
a) 80%
b) 85%
c) 75%
d) 70%
e) 60%
Solution:
Answer: C
Required % = 60/80 *100 = 75%
Thus, the required percentage is 75%.
19. Question
Find the average veg burger sold in A and B.
a) 44
b) 60
c) 72
d) 66
e) 45
Solution:
Answer: D
Required average = (72 + 60) /2 = 66
∴ The average veg burger sold by A and B is 66.
20. Question
Find the ratio between the burger sold in B to the veg burger sold in C.
a) 1: 2
b) 20: 9
c) 3: 4
d) 9: 20
e) 3: 16
Solution:
Answer: B
Required ratio = (60 + 80): 63 = 20: 9
Directions (21-24): Read the following tables carefully and answer the questions that are given below.
A number of contestants ( in lakh ) participating in a fashion designing show from six different cities named P, Q, R, S, T, and U. The successful and unsuccessful contestants ratio of the contestants are given below.
| City |
P
|
Q
|
R
|
S
|
T
|
U
|
| Number |
1.25 |
3.14 |
1.08 |
2.27 |
1.85 |
2.73 |
|
City
|
Successful
|
Unsuccessful
|
|
P
|
7
|
3
|
|
Q
|
5
|
3
|
|
R
|
4
|
5
|
|
S
|
1
|
3
|
|
T
|
3
|
2
|
|
U
|
7
|
5
|
21. Question:
The number of contestants participating in the fashion designing show from city R is what percent of the number of contestants participating in the show from city Q? (Approximate value.)
a) 34%
b) 44%
c) 54%
d) 40%
e) 50%
Sol.
Answer. A
Required percentage
=(1.08 × 100) / 3.14 %
= 34%
Thus the percentage is 34%.
22. Question
What is the respective ratio of the numbers of contestants unsuccessful in the show from city S to those unsuccessful in the show from city P?
a) 215 : 50
b) 221 : 75
c) 223 : 50
d) 227 : 50
e) None of these
Solution:
Answer. D
Required ratio
= (3/4 × 2.27) : (3/10 × 1.25)
= 1.7025 : 0.375
= 227 : 50
Thus, the required ratio is 227:50.
23. Question
The number of contestants qualifying the exam from city U is what percent of the total number of contestants participating from all the cities together? (Approximate value.)
a) 12.93%
b) 21.55%
c) 15.39%
d) 19.72%
e) 25.75%
Solution:
Answer : A
Required percentage
= (2.73 × 7/12) / (1.25 + 3.14 + 1.08 + 2.27 + 1.85 + 2.73) ×100 %
=(1.5925/12.32)× 100%
= 12.93 %
Thus, the required percentage is 12.93%.
24. Question
What is the number of unsuccessful contestants in city S?
a) 1.10 lakh
b) 1.5270 lakh
c) 1.7025 lakh
d) 1.9935 lakh
e) 3.99 lakh
Solution:
Answer: C
Number of unsuccessful contestants in city S
= (2.27 × 3/4) lakh
= 1.7025 lakh
∴ The number of unsuccessful contestants in city S = 1.7025 lakh
25. Question
A trader invests a sum of money in a scheme that offers 4% interest per annum with an increase of 0.5% per annum each year. If he received Rs. 9880 as interest at the end of 4 years, then find the money invested by the trader.
a) 42000
b) 45000
c) 47000
d) 48000
e) 52000
Solution:
Answer: E
(4% + 4.5% + 5% + 5.5%) = 19%
19% = 9880
100% = (9880 × 100) /19
= 52000
∴ Money invested by the trader = 52000
26. Question:
Price of a packet of biscuits Rs. 750 is offered at an 8% discount and the price of a packet of chocolate Rs. 1250 is offered at a 20% discount. If a man buys 5 packets of biscuits and 3 packets of chocolate, then what percentage effective discount does the man get?
a) 14%
b) 17%
c) 18%
d) 20%
e) 25%
Solution:
Answer: A
Total price of 5 packet biscuit and 3 packet chocolate
= (750 × 5) +(1250 × 3)
=7500
Discount in 5 packet Biscuit
= (750 × 5) × 8%
=300
Discount in 3 packet chocolate
= (1250 × 3) × 20%
=750
Total discount
= ( 300 + 750)
= 1050
Required Discount%
= (1050 ×100) /7500
=14%
∴ The man get the effective discount is 14%.
27. Question:
A vessel is full of 80 litres of fruit juice. 1/10 of total fruit juice is taken out and replaced by water. Again, the same amount of mixture was taken out and replaced by water. Find the amount of fruit juice in the final mixture so formed.
a) 50.50 litre
b) 56.20 litre
c) 60.50 litre
d) 64.80 litre
e) 70.50 litre
Solution:
Answer: D
1/10 × 80 = 8 litre
|
Initial (mixture)
|
Left (fruit juice)
|
|
80
|
72
|
|
10
|
9 (first time taken out)
|
|
10
|
9 (second time taken out)
|
|
Total – 100
|
81
|
Required fruit juice
= (80 × 81) /100
= 64.8 litre
∴ The amount of fruit juice in the final mixture is 64.8 litres.
28. Question
A train crosses a platform of length 400 meters in 15 sec and the same train crosses a pole in 10 sec. Find the time taken by the same train to cross a bridge of length 200 meters?
a) 12 sec
b) 12.50 sec
c) 15.50 sec
d) 22 sec
e) None of these
Solution:
Answer: B
Let, the length of the train is L meters
Speed = Distance/Time
(L + 400)/15 = L/10
15 L = 10 L + 4000
5 L = 4000
L = 800 meter
The time taken by the train to cross a bridge
Time = Distance/Speed
Required time
= (800 + 200)/(800/10)
= 1000/80
= 12.50 sec
Thus, the time taken by the train = 12.50 sec
29. Question
Amal and Bimal started a business in partnership. Amal invests certain money for one year and after 6 months, Bimal invests Rs. 4000 more than the investment of Amal. The ratio of annual total profit and Amal’s profit is 7:3. Find the investment of Amal.
a) 1200
b) 1400
c) 3600
d) 2400
e) 4800
Solution:
Answer: D
Let, Amal invest Rs. P
Therefore, Bimal invest Rs. = P + 4000
Hence, the ratio of Amal : Bimal’s investment is
= 12 × P : 6 ×(P + 4000)
= 2P : (P + 4000)
Now, according to question, the ratio of annual total investment and Amal’s investment,
2P/(3P + 4000) = 3/7
14P = 9P + 12000
5P = 12000
P = 2400
Therefore, the investment of Amal is Rs. 2400.
30. Question
Kapil and Vimal started work and will get money according to their efficiency. A certain amount is the wages for 28 days of Kapil’s work and it is equal to the wages of Vipul’s 21 days of work. That same amount is sufficient to pay the wages of both for how many days?
a) 12 days
b) 15 days
c) 6 days
d) 10 days
e) 8 days
Sol.
Answer: A
Let, the total work (LCM of 28 and 21) is = 84 unit
Within 1 day, Kapil can do = 84/28 = 3 unit
Within 1 day, Vipul can do = 84/21 = 4 unit
Within 1 day, both can work = (3 + 4) = 7 unit
Together, they can work in = 84/7 = 12 days.
Thus, the same amount of money is sufficient to pay for both in 12 days.
Directions ( 31 – 35):
There were four different banks named A, B, C, and D. These four banks opened a certain number of accounts in three years 2016, 2017, and 2018. The following graph shows the account opening in four different banks A, B, C, D over the year.
31. Question
The percentage increase in account opening by bank B from 2016 to 2017 is about
a) 30.8 %
b) 22.2 %
c) 18.2 %
d) 18.4 %
e) None of these
Sol.
Answer : B
Percentage increase
= {(55 – 45 )/45 } ×100
= 22.2 %
32. Question
Account opening by bank B in 2017 and by bank D in 2018 together is what percent of account opening by bank A in 2016?
a) 50 %
b) 200 %
c) 150 %
d) 75 %
e) None of these
Solution:
Answer: B
Account opening by bank B in 2017 and by bank D in 2018 together
= (55+65) = 120
Account opening by bank A in 2016 = 60
Required percentage
=(120 / 60 ) × 100 %
= 200 %
33. Question
Which one of the four banks has recorded the maximum percentage increase in account opening from 2017 to 2018?
a) A
b) B
c) C
d) D
e) None of these
Solution:
Answer : D
Bank A ={(75 – 70) / 70} × 100 %
=7.14 %
Bank B = negative
Bank C = negative
Bank D = {( 65 – 60 ) / 60} × 100 %
= 8.33 %
So, Maximum percentage increase in bank D.
34. Question
Which bank has recorded the maximum percentage increase in account opening from 2016 to 2017?
a) A
b) B
c) C
d) D
e) None of these
Solution:
Answer. C
Bank A = {( 70 – 60 ) / 60} × 100%
= 16.66 %
Bank B = {( 55 – 45 ) / 45 } × 100 %
= 22.2 %
Bank C = {( 85 – 65 ) / 65 } × 100 %
= 30.77 %
Bank D = {( 60 – 50 ) / 50 } × 100 %
= 20 %
So, the maximum percentage increase in bank C.
35. Question
Find the ratio between the average account opening by four banks in 2017 and average account opening by four banks in 2016 is
a) 25:22
b) 51:50
c) 11:15
d) 27:22
e) None of these
Solution:
Answer: D
In 2017 = ( 70 + 55 + 85 + 60 ) / 4
= 270/4
In 2016 = ( 60 + 45 + 65 + 50) / 4
= 55
Required ratio = 270/4 : 55 = 27:22
Thus, the ratio between the average account opening by four banks in 2017 and the average account opening by four banks in 2016 is 27:22.
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