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Directions (6 – 10): In the following questions, two equations I and II are given. You have to solve both the equations and give answer as,
If x > y
If x ≥ y
If x < y
If x ≤ y
If x = y or the relation cannot be established
1/x + 1/(x-10) = 8/75
132/y + 132/(y + 11) = 1
Correct
Answer: e)
I. 1/x + 1/(x-10) = 8/75
(2x – 10)/(x^{2} – 10x) = 8/75
75x – 375 = 4x^{2} – 40x
4x^{2} – 115x + 375 = 0
4x^{2} – 100x – 15x + 375 = 0
4x(x – 25) – 15 (x – 25) = 0
(4x – 15)(x – 25) = 0
X = 15/4, 25 = 3.75, 25
II. 132/y – 132/(y + 11) = 1
[132*(y + 11 – y)]/(y^{2} + 11y) = 1
132*11 = y^{2} + 11y
Y^{2} + 11y – 1452 = 0
(y – 33) (y + 44) = 0
Y = 33, -44
Can’t be determined
Incorrect
Answer: e)
I. 1/x + 1/(x-10) = 8/75
(2x – 10)/(x^{2} – 10x) = 8/75
75x – 375 = 4x^{2} – 40x
4x^{2} – 115x + 375 = 0
4x^{2} – 100x – 15x + 375 = 0
4x(x – 25) – 15 (x – 25) = 0
(4x – 15)(x – 25) = 0
X = 15/4, 25 = 3.75, 25
II. 132/y – 132/(y + 11) = 1
[132*(y + 11 – y)]/(y^{2} + 11y) = 1
132*11 = y^{2} + 11y
Y^{2} + 11y – 1452 = 0
(y – 33) (y + 44) = 0
Y = 33, -44
Can’t be determined
Question 7 of 20
7. Question
Directions (6 – 10): In the following questions, two equations I and II are given. You have to solve both the equations and give answer as,
If x > y
If x ≥ y
If x < y
If x ≤ y
If x = y or the relation cannot be established
x^{2} +18x +72 =0
y^{2} + 30y +56 =0
Correct
Answer: e)
I. x^{2} +18x +72 =0
(x+12)(x+6) =0
X= -12, -6
II. y^{2} + 30 y +56 =0
(y+28)(y+2) =0
Y= -28, -2
Can’t be determined
Incorrect
Answer: e)
I. x^{2} +18x +72 =0
(x+12)(x+6) =0
X= -12, -6
II. y^{2} + 30 y +56 =0
(y+28)(y+2) =0
Y= -28, -2
Can’t be determined
Question 8 of 20
8. Question
Directions (6 – 10): In the following questions, two equations I and II are given. You have to solve both the equations and give answer as,
If x > y
If x ≥ y
If x < y
If x ≤ y
If x = y or the relation cannot be established
2x^{2} – 9x +4 =0
y^{2} – 14y +40 =0
Correct
Answer: d)
I. 2x^{2} – 9x +4 =0
2x^{2} – x – 8x +4 =0
x (2x – 1) – 4 (2x – 1)=0
(x – 4) (2x – 1) = 0
x = 4, 1/2
II. y^{2} – 14y +40 =0
y^{2} -10y – 4y +40 =0
(y – 10) (y – 4) =0
y = 10, 4
x ≤ y
Incorrect
Answer: d)
I. 2x^{2} – 9x +4 =0
2x^{2} – x – 8x +4 =0
x (2x – 1) – 4 (2x – 1)=0
(x – 4) (2x – 1) = 0
x = 4, 1/2
II. y^{2} – 14y +40 =0
y^{2} -10y – 4y +40 =0
(y – 10) (y – 4) =0
y = 10, 4
x ≤ y
Question 9 of 20
9. Question
Directions (6 – 10): In the following questions, two equations I and II are given. You have to solve both the equations and give answer as,
If x > y
If x ≥ y
If x < y
If x ≤ y
If x = y or the relation cannot be established
4x^{2} -13x +10 =0
2y^{2} -15y +22 =0
Correct
Answer: d)
I. 4x^{2} -13x +10 =0
4x^{2} -8x-5x +10 =0
4x(x-2) – 5 (x-2) =0
(4x-5)(x – 2) =0
X = 5/4, 2
II. 2y^{2} -15y +22 =0
2y^{2} -4y-11y +22 =0
2y(y-2)-11 (y-2) =0
(2y-11)(y – 2) =0
Y=11/2, 2
x ≤ y
Incorrect
Answer: d)
I. 4x^{2} -13x +10 =0
4x^{2} -8x-5x +10 =0
4x(x-2) – 5 (x-2) =0
(4x-5)(x – 2) =0
X = 5/4, 2
II. 2y^{2} -15y +22 =0
2y^{2} -4y-11y +22 =0
2y(y-2)-11 (y-2) =0
(2y-11)(y – 2) =0
Y=11/2, 2
x ≤ y
Question 10 of 20
10. Question
Directions (6 – 10): In the following questions, two equations I and II are given. You have to solve both the equations and give answer as,
If x > y
If x ≥ y
If x < y
If x ≤ y
If x = y or the relation cannot be established
5x^{2} -28x +39 =0
2y^{2} -13y +20 =0
Correct
Answer: e)
I. 5x^{2} -28x +39 =0
5x^{2} -15x-13x +39 =0
5x(x-3)-13 (x-3) =0
(5x – 13)(x – 3) =0
X= 13/5, 3
II. 2y^{2} -13y +20 =0
2y^{2} -8y-5y +20 =0
2y(y-4)-5 (y-4) =0
(2y – 5) (y – 4) =0
Y=5/2, 4
Can’t be determined
Incorrect
Answer: e)
I. 5x^{2} -28x +39 =0
5x^{2} -15x-13x +39 =0
5x(x-3)-13 (x-3) =0
(5x – 13)(x – 3) =0
X= 13/5, 3
II. 2y^{2} -13y +20 =0
2y^{2} -8y-5y +20 =0
2y(y-4)-5 (y-4) =0
(2y – 5) (y – 4) =0
Y=5/2, 4
Can’t be determined
Question 11 of 20
11. Question
A and B can finish a work in 18 days while B and C can do it in 12 days. A started the work, worked for 6 days only and then B worked for 8 days and the remaining work was finished by C alone in 15 days. In how many days could C alone have finished the whole work?
Correct
Answer: d)
A and B can finish a work in 18 days = 1/A + 1/B = 1/18
B and C can do it in 12 days = 1/B + 1/C = 1/12
According to the question
6/A + 8/B + 15/C = 1
=> 6(1/A + 1/B) + 2(1/B + 1/C) + 13/C = 1
=> 6/18 + 2/12 + 13/C = 1
=> 13/C = 1 – 1/3 – 1/6
=> 13/C = (6 – 2 – 1)/6
=> (1/C) = (3/6)*(1/13) = 1/26
C alone can finish the whole work in 26 days
Incorrect
Answer: d)
A and B can finish a work in 18 days = 1/A + 1/B = 1/18
B and C can do it in 12 days = 1/B + 1/C = 1/12
According to the question
6/A + 8/B + 15/C = 1
=> 6(1/A + 1/B) + 2(1/B + 1/C) + 13/C = 1
=> 6/18 + 2/12 + 13/C = 1
=> 13/C = 1 – 1/3 – 1/6
=> 13/C = (6 – 2 – 1)/6
=> (1/C) = (3/6)*(1/13) = 1/26
C alone can finish the whole work in 26 days
Question 12 of 20
12. Question
A, B and C started a business by investing in the ratio of 3: 5: 7. After 5 months, A invested Rs. 15000 more. And after 3 months, C withdraws Rs. 30000. Find the initial investment of B, if the share of A, B and C is in the ratio of 45: 60: 76?
Correct
Answer: a)
The initial investment of A, B and C = 3x, 5x and 7x
Manoj marks an item one-fourth more than the CP and allows successive discounts of x% and (x+5) %. If the CP of an item is Rs. 500 and he losses 15 %, then find the value of ‘x’?
Correct
Answer: b)
SP = 500*(85/100) = 425
MP = 500*(5/4) = Rs. 625
According to the question,
625*[(100 – x)/100]*[(95 – x)/100] = 425
9500 – 100x – 95x + x^{2} = 6800
X^{2} – 195x + 2700 = 0
(x – 180) (x – 15) = 0
X = 180, 15 (180 should be eliminated)
X = 15 %
Incorrect
Answer: b)
SP = 500*(85/100) = 425
MP = 500*(5/4) = Rs. 625
According to the question,
625*[(100 – x)/100]*[(95 – x)/100] = 425
9500 – 100x – 95x + x^{2} = 6800
X^{2} – 195x + 2700 = 0
(x – 180) (x – 15) = 0
X = 180, 15 (180 should be eliminated)
X = 15 %
Question 14 of 20
14. Question
The difference between the ages of Yuvaraj and Ajay, 4 years ago was 8 years. If the ratio of their ages 7 years hence is 5: 4, then find the present age of Yuvaraj’s mother who is 25 years older than Yuvaraj?
Correct
Answer: c)
4 years ago, Yuvaraj – Ajay = 8
7 years hence, the ratio of Yuvaraj and Ajay = 5: 4 (5x, 4x)
Present age of Yuvaraj and Ajay = 5x – 7, 4x – 7
According to the question,
5x – 4x = 8
x = 8
Present age of Yuvaraj = 5x – 7 = 33
Present age of Yuvaraj’s mother = 33 + 25
= > 58 years
Incorrect
Answer: c)
4 years ago, Yuvaraj – Ajay = 8
7 years hence, the ratio of Yuvaraj and Ajay = 5: 4 (5x, 4x)
Present age of Yuvaraj and Ajay = 5x – 7, 4x – 7
According to the question,
5x – 4x = 8
x = 8
Present age of Yuvaraj = 5x – 7 = 33
Present age of Yuvaraj’s mother = 33 + 25
= > 58 years
Question 15 of 20
15. Question
A and B together can complete a work in 35 days, while A is 40 % more efficient than B, then find in how many days the work will be complete if they work on alternative days starting with A?
Correct
Answer: a)
Efficiency of A and B = 140: 100 = 7: 5
The ratio of time taken by A and B = 5: 7 (5x, 7x)
(1/5x) + (1/7x) = 1/35
12x/(5x*7x) = 1/35
X = 12
The time taken by A and B = 5x, 7x = 60 and 84 days
Total units = 420 (LCM of 60, 84)
A’s one day work = 7 units
B’s one day work = 5 units
Work done in 2 days = 7 + 5 = 12 units
Work done in 70 days = 12*35 = 420 units
Work will be completed in 70 days
Incorrect
Answer: a)
Efficiency of A and B = 140: 100 = 7: 5
The ratio of time taken by A and B = 5: 7 (5x, 7x)
(1/5x) + (1/7x) = 1/35
12x/(5x*7x) = 1/35
X = 12
The time taken by A and B = 5x, 7x = 60 and 84 days
Total units = 420 (LCM of 60, 84)
A’s one day work = 7 units
B’s one day work = 5 units
Work done in 2 days = 7 + 5 = 12 units
Work done in 70 days = 12*35 = 420 units
Work will be completed in 70 days
Question 16 of 20
16. Question
Directions (16 – 20): Study the following information carefully and answer the question given below.
The following table represents the number of students enrolled in six different colleges, percentage of students left the college and percentage of students who passed out the college among those who continued their study in the college.
Find the sum of total number of students from all the colleges, who continued their study.
Correct
Answer: c)
A = (100 – 5)/100 x 1400 = 1330
B = (100 – 8)/100 x 1250 = 1150
C = (100 – 12)/100 x 1550 = 1364
D = (100 – 10)/100 x 900 = 810
E = (100 – 15)/100 x 1300 = 1105
F = (100 – 4)/100 x 1500 = 1440
Required No of students = 1330 + 1150 + 1364 + 810 + 1105 + 1440 = 7199
Incorrect
Answer: c)
A = (100 – 5)/100 x 1400 = 1330
B = (100 – 8)/100 x 1250 = 1150
C = (100 – 12)/100 x 1550 = 1364
D = (100 – 10)/100 x 900 = 810
E = (100 – 15)/100 x 1300 = 1105
F = (100 – 4)/100 x 1500 = 1440
Required No of students = 1330 + 1150 + 1364 + 810 + 1105 + 1440 = 7199
Question 17 of 20
17. Question
Directions (16 – 20): Study the following information carefully and answer the question given below.
The following table represents the number of students enrolled in six different colleges, percentage of students left the college and percentage of students who passed out the college among those who continued their study in the college.
Number of students passed from college B is approximately what percent of the number of students passed from college D?
Correct
Answer: b)
Number of students who continued study in B = (100 – 8)/100 x 1250 = 1150
Passed Students = 76/100 x 1150 = 874
Number of students who continued study in D = (100 – 10)/100 x 900 = 810
Directions (16 – 20): Study the following information carefully and answer the question given below.
The following table represents the number of students enrolled in six different colleges, percentage of students left the college and percentage of students who passed out the college among those who continued their study in the college.
Total number of students enrolled in A and B together is what percent more than the number of students enrolled in C and D together?
Correct
Answer: b)
Total number of students enrolled in A and B together = 1400 + 1250 = 2650
Total number of students enrolled in C and D together = 1550 + 900 = 2450
Required percentage = (2650 – 2450)/2450 x 100 = 8.163%
Incorrect
Answer: b)
Total number of students enrolled in A and B together = 1400 + 1250 = 2650
Total number of students enrolled in C and D together = 1550 + 900 = 2450
Required percentage = (2650 – 2450)/2450 x 100 = 8.163%
Question 19 of 20
19. Question
Directions (16 – 20): Study the following information carefully and answer the question given below.
The following table represents the number of students enrolled in six different colleges, percentage of students left the college and percentage of students who passed out the college among those who continued their study in the college.
Find the ratio of number of failed students of college C and college F respectively.
Correct
Answer: c)
Number of students who continued study in C = (100 – 12)/100 x 1550 = 1364
Failed = (100-75)/100 x 1364 = 341
Number of students who continued study in F = (100 – 4)/100 x 1500 = 1440
Failed = (100 – 90)/100 x 1440 = 144
Required ratio = 341: 144
Incorrect
Answer: c)
Number of students who continued study in C = (100 – 12)/100 x 1550 = 1364
Failed = (100-75)/100 x 1364 = 341
Number of students who continued study in F = (100 – 4)/100 x 1500 = 1440
Failed = (100 – 90)/100 x 1440 = 144
Required ratio = 341: 144
Question 20 of 20
20. Question
Directions (16 – 20): Study the following information carefully and answer the question given below.
The following table represents the number of students enrolled in six different colleges, percentage of students left the college and percentage of students who passed out the college among those who continued their study in the college.
Passed students of college A is approximately what percent of failed students of college C?
Correct
Answer: d)
Number of students who continued their study from college A = (100 – 5)/100 x 1400 = 1330
Passed = 80/100 x 1330 = 1064
Number of students who continued their study from college C
5) 34478 ÷ 8 + (3/13) of 12154 + 30 % of 599 =?^{2} – 274
a) 93
b) 74
c) 87
d) 68
e) 82
Directions (6 – 10): In the following questions, two equations I and II are given. You have to solve both the equations and give answer as,
If x > y
If x ≥ y
If x < y
If x ≤ y
If x = y or the relation cannot be established
6) I. 1/x + 1/(x-10) = 8/75
II. 132/y + 132/(y + 11) = 1
7) I. x^{2} +18x +72 =0
II. y^{2} + 30y +56 =0
8) I. 2x^{2} – 9x +4 =0
II. y^{2} – 14y +40 =0
9) I. 4x^{2} -13x +10 =0
II. 2y^{2} -15y +22 =0
10) I. 5x^{2} -28x +39 =0
II. 2y^{2} -13y +20 =0
11) A and B can finish a work in 18 days while B and C can do it in 12 days. A started the work, worked for 6 days only and then B worked for 8 days and the remaining work was finished by C alone in 15 days. In how many days could C alone have finished the whole work?
a) 22 days
b) 20 days
c) 18 days
d) 26 days
e) None of these
12) A, B and C started a business by investing in the ratio of 3: 5: 7. After 5 months, A invested Rs. 15000 more. And after 3 months, C withdraws Rs. 30000. Find the initial investment of B, if the share of A, B and C is in the ratio of 45: 60: 76?
a) Rs. 75000
b) Rs. 90000
c) Rs. 65000
d) Rs. 80000
e) None of these
13) Manoj marks an item one-fourth more than the CP and allows successive discounts of x% and (x+5) %. If the CP of an item is Rs. 500 and he losses 15 %, then find the value of ‘x’?
a) 18 %
b) 15 %
c) 12 %
d) 20 %
e) None of these
14) The difference between the ages of Yuvaraj and Ajay, 4 years ago was 8 years. If the ratio of their ages 7 years hence is 5: 4, then find the present age of Yuvaraj’s mother who is 25 years older than Yuvaraj?
a) 64 years
b) 72 years
c) 58 years
d) 54 years
e) None of these
15) A and B together can complete a work in 35 days, while A is 40 % more efficient than B, then find in how many days the work will be complete if they work on alternative days starting with A?
a) 70 days
b) 60 days
c) 55 days
d) 66 days
e) None of these
Directions (16 – 20): Study the following information carefully and answer the question given below.
The following table represents the number of students enrolled in six different colleges, percentage of students left the college and percentage of students who passed out the college among those who continued their study in the college.
16) Find the sum of total number of students from all the colleges, who continued their study.
a) 7432
b) 7223
c) 7199
d) 7351
e) None of these
17) Number of students passed from college B is approximately what percent of the number of students passed from college D?
a) 152
b) 180
c) 187
d) 125
e) None of these
18) Total number of students enrolled in A and B together is what percent more than the number of students enrolled in C and D together?
a) 6.134%
b) 8.163%
c) 9.156%
d) 4.146%
e) 7. 178%
19) Find the ratio of number of failed students of college C and college F respectively.
a) 1137: 450
b) 960: 1457
c) 341: 144
d) 450: 137
e) None of these
20) Passed students of college A is approximately what percent of failed students of college C?