51. Find the value of K?

Statement I: Jagan invested 2/3rd of his income in a simple interest scheme at 16% per annum for K years and the remaining amount is invested in a compound interest scheme at 40% per annum for 2 years.

Statement II: If the interest received by Jagan in the simple interest scheme is equal to the interest received by Jagan in the compound interest scheme.

A. 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. 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. The data either in statement I alone or in statement II alone is sufficient to answer the question
D. The data given in both statements I and II together are not sufficient to answer the question
E. The data given in both statements I and II together are necessary to answer the question.

Option “E” is correct.

Answer: E

From statement I,

Let the total income of Jagan = 3x

The total amount invested by Jagan in the simple interest = 2x

The total amount invested by Jagan in the compound interest = 3x – 2x = 1x

So, Statement I alone is not sufficient to answer the question.

From statement II,

The interest received by Jagan in the simple interest scheme is equal to the interest received by Jagan in the compound interest scheme

So, Statement II alone is not sufficient to answer the question.

From statement I and II,

2x * 16 * K/100 = (x * (1+40/100)2 – x)

K * 2x * 16/100 = 49x/25 – x

K = 24x/25 * 100/16 *1/2x

K = 3

Both statements are necessary to answer the question.

52. If one bottle is drawn at random from box B1 and then find the probability of picking a green bottle?

Statement I: The total number of bottles in box B1 is 25% more than the total number of bottles in box B2. The number of orange bottles in box B2 is 16.

Statement II: Ratio of the number of orange to green bottles in boxes B1 and B2 is 2:1 and 4:3 respectively.

A. 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. 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. The data either in statement I alone or in statement II alone is sufficient to answer the question
D. The data given in both statements I and II together are not sufficient to answer the question
E. The data given in both statements I and II together are necessary to answer the question.

Option “D” is correct.

Answer: D

From statement I,

The total number of bottles in box B2 = 4x

The total number of bottles in box B1 = 4x * 125/100 = 5x

So, Statement I alone is not sufficient to answer the question.

From statement II,

The total number of bottles is not given.

So, Statement II alone is not sufficient to answer the question.

53. Find the speed of the boat in still water?

Statement I: Ratio of the downstream and upstream speed of the boat is 2:1 and the speed of the stream is 10 km//hr.

Statement II: The boat covers 200 km downstream in 5 hours and the same boat covers the same distance upstream in 10 hours.

A. 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. 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. The data either in statement I alone or in statement II alone is sufficient to answer the question
D. The data given in both statements I and II together are not sufficient to answer the question
E. The data given in both statements I and II together are necessary to answer the question.

Option “C” is correct.

Answer: C

From statement I,

Let the downstream speed of the boat = 2x

And the upstream speed of the boat = 1x

The speed of the boat in still water = (2x + 1x)/2 = 3x/2 = 1.5x

The speed of the stream =(2x – 1x)/2 = x/2

x/2 = 10

x = 20 km/hr

The speed of the boat in still water = 20 * 1.5 = 30 km/hr

So, Statement I alone is sufficient to answer the question.

From statement II,

The downstream speed of the boat = 200/5 = 40 km/hr

The upstream speed of the boat = 200/10 = 20 km/hr

The speed of the boat in still water = (40 + 20)/2 = 60/2 = 30 km/hr

So, Statement II alone is sufficient to answer the question.

So, either statement I alone or statement II alone is sufficient to answer the question

54. Find the present age of C?

Statement I: Ratio of the present age of A and B is 5: 8 and after 5 years, the average age of A, B and C is 39 years.

Statement II: The sum of the present age of A and C is 62 years and C is 12 years older than A.

A. 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. 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. The data either in statement I alone or in statement II alone is sufficient to answer the question
D. The data given in both statements I and II together are not sufficient to answer the question
E. The data given in both statements I and II together are necessary to answer the question.

Option “B” is correct.

Answer: B

From statement I,

Let the present age of A = 5x

And the present age of B = 8x

The present age of A, B and C = 39 * 3 – 5 * 3 = 102 years

So, Statement I alone is not sufficient to answer the question.

From statement II,

A + C = 62 years

C – A = 12

2C = 74

C = 37 years

So, Statement II alone is sufficient to answer the question.

55. In how many days C alone complete work?

Statement I: A alone can do a piece of work in 24 days and the efficiency of B is 80% of the efficiency of A. If A, B and C together can complete the work in 10 days.

Statement II: A and C together complete the work in 15 days and B and D together complete the work in 20 days.

A. 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. 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. The data either in statement I alone or in statement II alone is sufficient to answer the question
D. The data given in both statements I and II together are not sufficient to answer the question
E. The data given in both statements I and II together are necessary to answer the question.

Option “A” is correct.

Answer: A

From statement I,

A alone complete the work = 24 days

Efficiency ratio of A and B = 100 : 80 = 5:4

Time ratio of A and B = 4:5

B alone complete the work = 24 * 5/4 = 30 days

C alone complete the work = C days

1/A + 1/B + 1/C = 1/10

1/24 + 1/30 + 1/C= 1/10

1/C = (12 – 5 – 4)/120

1/C = 3/120

1/C = 1/40

So, Statement I alone is sufficient to answer the question.

From statement II,

1/A + 1/C = 1/15

1/B + 1/D = 1/20

So, Statement II alone is not sufficient to answer the question.

56. What is the length of train B?

Statement I: Train A crosses a platform of length 200 m in 24 seconds and the ratio of the length of Train A and Train B is 4:3.

Statement II: Train A crosses an electric pole in 16 seconds and crosses a bridge in 40 seconds.

A. 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. 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. The data either in statement I alone or in statement II alone is sufficient to answer the question
D. The data given in both statements I and II together are not sufficient to answer the question
E. The data given in both statements I and II together are necessary to answer the question.

Option “E” is correct.

Answer: E

From statement I,

Length of Train A = 4x

Length of Train B = 3x

Speed of Train A = (4x + 200)/24

So, Statement I alone is not sufficient to answer the question.

From statement II,

Train A crosses an electric pole in 16 seconds and crosses a bridge in 40 seconds.

So, Statement II alone is not sufficient to answer the question.

From Statement I and II,

(4x + 200)/24 = 4x/16

x = 100 m

Length of Train B = 3 * 100 = 300 m

So, both statements are necessary to answer the question.

57. Find the total time taken by Pipe A and Pipe B to fill the tank.

Statement I: Pipe A alone can fill the tank in 30 hours and the ratio of the efficiency of Pipe A and B is 1:2.

Statement II: Pipe B alone can fill the tank in 25 hours.

A. 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. 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. The data either in statement I alone or in statement II alone is sufficient to answer the question
D. The data given in both statements I and II together are not sufficient to answer the question
E. The data given in both statements I and II together are necessary to answer the question.

Option “A” is correct.

Answer: A

From statement I,

Pipe A alone can fill the tank in 30 hours

Efficiency Pipe A and Pipe B is 1:2

Time taken ratio of Pipe A and Pipe B = 2:1

Pipe B alone can fill the tank = 30 * 1/2 = 15 hours

(1/A) + (1/B) = 1/30 + 1/15 = 3/30 = 1/10 = 10 hours

So, Statement I alone is sufficient to answer the question.

From statement II,

Pipe B alone can fill the tank in 25 hours

So, Statement II alone is not sufficient to answer the question.

58. Find the investment of A.

Statement I: A gains a compound interest of Rs.1500 at R% per annum for 2 years.

Statement II: A invested Rs.x in Simple interest at 30% per annum for 3 years and gains an interest of Rs.1350.

A. 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. 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. The data either in statement I alone or in statement II alone is sufficient to answer the question
D. The data given in both statements I and II together are not sufficient to answer the question
E. The data given in both statements I and II together are necessary to answer the question.

Option “B” is correct.

Answer: B

From statement I,

A gains a compound interest of Rs.1500 at R% per annum for 2 years.

So, Statement I alone is not sufficient to answer the question.

From statement II,

x * 30 * 3/100 = 1350

x = Rs.1500

So, Statement II alone is sufficient to answer the question.

59. Find the sum of the speed of Boat P and Boat Q in still water.

Statement I: Boat P covers 300 km downstream in 10 hours and Boat Q covers 450 km upstream in 15 hours in the same stream and the ratio of the speed of the Boat P and Boat Q in still water is 5:7.

Statement II: Boat Q covers 440 km downstream in 11 hours and covers 420 km upstream in 14 hours and the speed of Boat P is 10 km/hr less than the speed of Boat Q.

A. 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. 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. The data either in statement I alone or in statement II alone is sufficient to answer the question
D. The data given in both statements I and II together are not sufficient to answer the question
E. The data given in both statements I and II together are necessary to answer the question.

Option “C” is correct.

Answer: C

From statement I,

Speed of Boat P = 5x km/hr

Speed of Boat Q = 7x km/hr

Speed of the current = C km/hr

300/(5x + C) = 10

5x + C = 30 — (1)

450/(7x – C) = 15

7x – C = 30 — (2)

From (1) and (2),

12x = 60

x = 5

Sum of the speed of Boat P and Boat Q in still water = 5 * 5 + 7 * 5 = 60 km/hr

So, statement I alone is sufficient to answer the question

From statement II,

Speed of Boat Q = x km/hr

Speed of the current = C km/hr

440/(x + C) = 11

x + C = 40 — (1)

420/(x – C) = 14

x – C = 30 — (2)

From (1) and (2),

2x = 70

x = 35 km/hr

Speed of Boat P = 35 – 10 = 25 km/hr

Required sum = 35 + 25 = 60 km/hr

So, either statement I alone or statement II alone is sufficient to answer the question

60. Find the present age of A.

Statement I: The ratio of age of A after 6 years and the age of B before 4 years is 7:8.

Statement II: The ratio of age of B after 4 years and the age of C after 6 years is 5:6 and the present age of C is 10 years more than that of D.

A. 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. 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. The data either in statement I alone or in statement II alone is sufficient to answer the question
D. The data given in both statements I and II together are not sufficient to answer the question
E. The data given in both statements I and II together are necessary to answer the question.

Option “D” is correct.

Answer: D

From statement I,

Present age of A = a

Present age of B = b

(a + 6)/(b – 4) = 7/8

So, Statement I alone is not sufficient to answer the question.

From statement II,

Present age of A = a

Present age of B = b

Present age of C = c

Present age of D = d

(b + 4)/(c + 6) = 5/6

c = d + 10

So, Statement II alone is not sufficient to answer the question.

 

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