Statement I: Ratio of age of A, B after 5 years is 5:7, and ratio of ages of A, C before 5 years is 5:3. Sum of the age of B after 5 years and C before 5 years is 44 years.
Statement II: Ratio of A and C after 7 years is 9:7, Sum of the present age of A and C is 34
A. The data given in both statements I and II together are not sufficient to answer the question
B. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
C. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
D. The data given in both statements I and II together are necessary to answer the question
E. The data either in statement I alone or in statement II alone is sufficient to answer the question
Option “E” is correct.
Answer: E
From statement I,
A’s present age = 5x-5, B’s present age = 7x-5
A’s present age = 5y+5 , C’s present age = 3y+5
5x-5 = 5y+5
x – y = 2
7x+3y =44
solving this, A’s present age=20
From statement II,
A’s present age = 9x-7 , C’s present age = 7x-7
9x-7 + 7x-7 = 34
16x =48
x=3
9x-7 = 20
Therefore, either statement I or II is sufficient to answer this question
2. A Bag contains ‘x’ red balls, 7 yellow balls, 8 green balls. Find the total number of balls in the bag.
Statement I: If two balls are taken at random, the probability of that balls being red is 1/19
Statement II: If two balls are taken at random, the probability of balls being green is 14/95
A. The data given in both statements I and II together are not sufficient to answer the question
B. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
C. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
D. The data given in both statements I and II together are necessary to answer the question
E. The data either in statement I alone or in statement II alone is sufficient to answer the question
Option “E” is correct.
Answer: E
From statement I,
Let no of Red balls = R (Therefore total balls = 15+R)
R=5
Total number of balls =20
Either Statement I or II is sufficient to answer this question.
3. What is the volume of the sphere?
Statement I: Radius of the cylinder is equal to the radius of the sphere and the volume of the cylinder is 2772 cm3.
Statement II: Volume of the cone is 308 cm3 and the height of the cone is 1 cm less than the radius of the cone and the radius of the cone is equal to the radius of the sphere.
A. The data given in both statements I and II together are not sufficient to answer the question
B. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
C. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
D. The data given in both statements I and II together are necessary to answer the question
E. The data either in statement I alone or in statement II alone is sufficient to answer the question
Option “B” is correct.
Answer: B
From statement I,
Radius of the cylinder is equal to the radius of the sphere and the volume of the cylinder is 2772 cm^{3}.
So, Statement I alone is not sufficient to answer the question.
From statement II,
308 = 1/3 * 22/7 * r * r * (r – 1)
294 = r^{3} – r^{2}
r = 7 cm
Volume of the sphere = 4/3 * 22/7 * 7 * 7 * 7 = 4312/3 cm^{3}
So, Statement II alone is sufficient to answer the question.
4. What is the length of train A?
Statement I: Train A crosses train B running in opposite direction in 18 seconds. Train B crosses a 500 m long bridge in 48 seconds and also crosses a man standing in a platform in 18 seconds.
Statement II: Train A crosses a platform of length 150 m and train C having length 250 m running in opposite direction in 24 seconds and 21 seconds respectively.
A. The data given in both statements I and II together are not sufficient to answer the question
B. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
C. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
D. The data given in both statements I and II together are necessary to answer the question
E. The data either in statement I alone or in statement II alone is sufficient to answer the question
Option “D” is correct.
Answer: D
From statement I,
Length of train A = x
Speed of train A = y
Speed of train B = z
Length of train B = b
x + b = (y + z) * 5/18 * 18
x + b = 5y + 5z
b + 500 = z * 5/18 * 48
3b + 1500 = 40z
b = z * 5/18 * 18
b = 5z
3b + 1500 = 8b
b = 300
z = 300/5 = 60
So, Statement I alone is not sufficient to answer the question.
From statement II,
Length of train A = x
Speed of train A = y
Speed of train C = c
x + 150 = y * 5/18 * 24
3x + 450 = 20y
x + 250 = (y + c) * 5/18 * 21
So, Statement II alone is not sufficient to answer the question.
5. Dinesh and Ramesh entered into a partnership with an investment in the ratio 7 : 5 respectively. After one year, Tanish joined them with investment equal to average of the initial investments of Dinesh and Ramesh. After one more year, Ramesh invested Rs. 20000 more. At the end of three years, they earned a total profit of Rs. 156000. Find the share of Ramesh in the profit.
Statement I: Respective ratio of the profit shares of Ramesh and Tanish is 19:12.
Statement II: Share of Dinesh in the profit is Rs. 63000.
A. The data given in both statements I and II together are not sufficient to answer the question
B. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
C. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
D. The data given in both statements I and II together are necessary to answer the question
E. The data either in statement I alone or in statement II alone is sufficient to answer the question
Option “C” is correct.
Answer: C
Let, initial amounts invested by Dinesh and Ramesh be Rs.7k and Rs.5k respectively.
Ratio of shares in the profit:
Dinesh : Ramesh : Tanish = (7k x 3) : (5k x 2 + 5k + 20000) : (6k x 2)
= 21k : (15k + 20000) : 12k ————— (i)
From Statement I:
(15k + 20000)/12k = 19/12
=> 19k = 15k + 20000
=> 19k – 15k = 20000
=> 4k = 20000
=> k = 20000/4
=> k = 5000
From (i)
Dinesh : Ramesh : Tanish = (21 x 5000) : (15 x 5000 + 20000) : (12 x 5000)
= 105000 : 95000 : 60000
= 21 : 19 : 12
Share of Ramesh in the profit = [19/(21 + 19 + 12)] x 156000
= (19/52) x 156000
= Rs. 57000
From Statement II:
[21k/(21k + 15k + 20000 + 12k)] x 156000 = 63000
=> 21k/(48k + 20000) x 52 = 21
=> 1092k = 1008k + 420000
=> 1092k – 1008k = 420000
=> 84k = 420000
=> k = 420000/84
=> k = 5000
From (i)
Dinesh: Ramesh: Tanish = (21 x 5000): (15 x 5000 + 20000): (12 x 5000)
= 105000: 95000: 60000
= 21: 19: 12
Share of Ramesh in the profit = [19/(21 + 19 +12)] x 156000
= (19/52) x 156000
= Rs. 57000
Hence, data in either in statement I alone or in statement II alone is sufficient to answer the question.
6. Find the difference between compound interest and simple interest on Rs. P at r % per annum after two years.
Statement I: Simple interest on Rs. P at r% per annum after five years will be Rs.24000.
Statement II: The total amount on compound interest of Rs. 50000 at r% per annum after two years will be Rs. 58320.
A. If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
B. If the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.
C. If the data in either in statement I alone or in statement II alone is sufficient to answer the question.
D. If the data in both the statements I and II together are not sufficient to answer the question.
E. If the data in both the statements I and II together are necessary to answer the question.
Option “E” is correct.
Answer: E
From Statement I:
We know that
SI = (P x r x t)/100
=> 24000 = (P x r x 5)/100
=> P x r = 2400000/5
=> P x r = 480000
From Statement II:
We know that
Amount on CI = P x (1 + r/100)^{t}
=>58320 = 50000 x (1 + r/100)^{2}
=>58320/50000 = (1 + r/100)^{2}
=> 729/625 = (1 + r/100)^{2}
=> (27/25)^{2} = (1 + r/100)^{2}
=> 27/25 = 1 + r/100
=> 27/25 – 1 = r/100
=> (27 – 25)/25 = r/100
=> 2 = r/4
=> r = 8%
From Statement I and II:
P x 8 = 480000
=> P = Rs. 60000
We know that, for two years
CI – SI = P x (r/100)^{2}
= > 60000 x (8/100)^{2}
= > 60000 x (8/100) x (8/100)
= > Rs. 384
Hence, data in both the statements I and II together are necessary to answer the question.
7. Find the share of C?
I) A, B and C started a business by investing Rs. 20000, Rs. 30000 and Rs. 40000 respectively. After 7 months, A invested Rs. 10000 more but C withdraw Rs. 10000. The total profit at the end of the year is Rs. 108000
II) A and C enter into a partnership by investing Rs. 30000 and Rs. 40000 respectively. After 4 months, B entered into a partnership by investing Rs. 50000.
A. Either statement I or statement II is sufficient
B. Only statement I is sufficient
C. Only statement II is sufficient
D. Both the statements I and II together are sufficient
E. Neither statement I nor statement II is sufficient
Only statement I alone is sufficient to answer the question.
8. How long will 15 women and 6 men take to do the work?
I) 6 women and 8 men can do a work in 4 days.
II) 9 women and 10 men can do the same work in 3 days.
A. Either statement I or statement II is sufficient
B. Only statement I is sufficient
C. Only statement II is sufficient
D. Both the statements I and II together are sufficient
E. Neither statement I nor statement II is sufficient
Option “D” is correct.
Answer: D
From statement I,
6 women and 8 men can do a work in 4 days
This statement alone is not sufficient to answer the question.
From statement II,
9 women and 10 men can do the same work in 3 days
This statement alone is not sufficient to answer the question.
From statement I and II,
Total work = (men (or) women) * days
Work equal. So,
(6w + 8m) * 4 = (9w + 10m) * 3
24w + 32m = 27w + 30m
2m = 3w
15w + 6m = 10m + 6m = 16 m
6w + 8m = 4m + 8m = 12 m
Men days
12 4
16 ?
(12 * 4) = (16 * x)
x = 3 days
Both the Statement I and II are sufficient to answer the question.
9. Find the age of Neelima after six years.
Statement I: Average of the present ages of Neelima, Sekhar and Sikha is 20 years. Respective ratio of the ages of Sekhar and Sikha before five years was 3:4.
Statement II: Respective ratio of the ages of Sekhar and Sikha after five years will be 5:6.
A. If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
B. If the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.
C. If the data in either in statement I alone or in statement II alone is sufficient to answer the question
D. If the data in both the statements I and II together are not sufficient to answer the question
E. If the data in both the statements I and II together are necessary to answer the question.
Option “E” is correct.
Answer: E
From Statement I:
Neelima + Sekhar + Sikha = 3 x 20 = 60
Respective ratio of the ages of Sekhar and Sikha before five years was 3:4.
From Statement II:
Respective ratio of the ages of Sekhar and Sikha after five years will be 5:6.
From Statement I and II:
Let, ages of Sekhar and Sikha before five years be 3k years and 4k years respectively.
(3k + 10)/(4k + 10) = 5/6
=> 18k + 60 = 20k + 50
=> 20k – 18k = 60 – 50
=> 2k = 10
=> k = 5
Present age of Sekhar = 3k + 5 = 3 x 5 + 5 = 20 years
Present age of Sikha = 4k + 5 = 4 x 5 + 5 = 25 years
Neelima + Sekhar + Sikha = 3 x 20 = 60
=>Neelima + 20 + 25 = 60
=>Neelima = 60 – 45
=>Neelima = 15
Age of Neelima after six years = 15 + 6 = 21 years
Hence, data in both the statements I and II together are necessary to answer the question.
10. The number of employees in company A is 5400. What is the ratio of the number of male employees in B to the number of female employees in B?
Statement I: The number of male employees in B is 11% more than the number of male employees in A and the number of female employees in B is 17% more than the number of female employees in B.
Statement II: The number of female employees in B is 612 more than the total number of female employees in A.
A. If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
B. If the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.
C. If the data in either in statement I alone or in statement II alone is sufficient to answer the question
D. If the data in both the statements I and II together are not sufficient to answer the question
E. If the data in both the statements I and II together are necessary to answer the question.
Option “E” is correct.
Answer: E
From statement I,
Number of employees in A = 5400
Number of female employees in A = x
Number of male employees in A = y
Number of male employees in B = y * 111/100
Number of female employees in B = x * 117/100
So, Statement I alone is not sufficient to answer the question.
From statement II,
Number of female employees in B – number of female employees in A = 612
So, Statement II alone is not sufficient to answer the question.
From statement I and II,
117x/100 – x = 612
17x = 61200
x = 3600
Number of male employees in A = 5400 – 3600 = 1800
Required ratio = 1800 * 111/100: 3600 * 117/100
= 37: 78
Both statements are necessary to answer the question.