Directions: The question consists of three statements numbered “I, II and III” given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.
1) What is the length of train A?
Statement 1: The ratio of the speed of Train A and Train B is 11:16
Statement 2: The length of Train B is 180 m and the difference between their speeds is 10 km/hr Statement 3: Train A and Train B running in the opposite directions and they cross each other in 20 seconds
A. The data in statements I and statements II are 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 statements I and III are not sufficient to answer the question.
C. The data in either statement I alone or in statement II alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
D. The data in all statements I, II and III is not sufficient to answer the question.
E. The data in all the statements I, II and III together are necessary to answer the question.
Sol:
From Statement 1
We have a speed ratio only 11: 16
So, statement 1 alone is not sufficient to answer
this question
From statement 2
Length of Train Y 180m and the speed
difference is 5 km/hr
So, statement 2 alone is not sufficient to answer
this question
From statement 3
Speed = Length of Train A + length of Train B /
time
So, Statement 3 alone is not sufficient to answer
this question
From 1 and 2
16x – 11x = 10
X = 2
Speed of Train A = 11*2 = 22 km/hr
Speed of Train B = 16*2 = 32 km/hr
From combining (I) (ii) and (iii)
Relative speed of the trains = length / 20
(22+32) * 5/18 = Train A + 180 / 20
15 * 20 = Train A + 180
Train A = 120 m
Hence, all the Statements are necessary to
answer this question.
2) Find the present age of B?
Statement 1: The ratio of the present age of A and B is 4 : 5 and the age of A, 8 years from now will be 1.5 times the age of B, 4 years ago. Statement 2: Average age of B and C, 6 years from now is 30 years
Statement 3: When B was born, the age of C is 8 years at that time.
A. The data in statements I and statements II are sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
B. The data in either statement II alone is sufficient to answer the question, while the data in statements I and III are not sufficient to answer the question.
C. The data in statement I alone or in statement II alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
D. The data in Statement I alone or Statement 2 and statement 3 together is sufficient to answer the question
E. The data in all the statements I, II and III together is necessary to answer the question.
Sol:
From Statement 1
The present age of A and B = 4x: 5x
4x + 8 = 1.5 (5x – 4)
X = 4
B = 5*4 = 20 years
So, Statement 1 alone is sufficient
From statement 2
Average age of B and C = 30
Total age = 30*2 = 60 years (6 years from now)
Present age of B and C = 60 – 12 = 48 years
So, statement 2 alone is not sufficient to answer
this question
From statement 3
The age difference of B and C is 8 years
So, statement 3 alone is not sufficient to answer
this question
Combining (II) and (III)
C + B = 48
C – B = 8
Then 2C = 56 => C = 28 and B = 20
Age of B = 20 years
Hence, statement 1 alone or statement 2 and
statement 3 together is sufficient to answer this
question
