question: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, which A and C together can do it in 2 hours. How long will B alone take to do it?
Options:
(A) 15 hours
(B) 14 hours
(C) 12 hours
(D) 74 hours
(E) 79 hours
answer: Stream of consciousness: A's 1 hour work = 1/4;
(B + C)'s 1 hour work = 1/3;
(A + C)'s 1 hour work = 1/2
(A + B + C)'s 1 hour work = (1/4 + 1/3) = 7/12
B's 1 hour work = (7/12 + 1/2) = 1/12
B alone will take 12 hours to do the work. The answer is (C).

q: A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 20 seconds. What is the length of the platform in meters?
Options:
(A) 200 meters
(B) 360 meters
(C) 420 meters
(D) 600 meters
(E) Cannot be determined
a: Stream of consciousness: Speed of the train in metres/sec = 72000/3600 = 20
Distance travelled by train to cross the platform = 30 * 20 = 600 = Length of train + Length of platform
Distance travelled by train to cross the man = 20 * 20 = 400 = Length of train
Length of platform = 600 - 400 = 200 The answer is (A).

question: In how many different ways can the letters of the word 'PREPTY' be arranged?
Options:
(A) 120
(B) 230
(C) 330
(D) 340
(E) 360
answer: Stream of consciousness: Number of ways = 61/21 6X5X4X3X2X1 - 360 The answer is (E).

q: From among the 36 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
Options:
(A) 1360
(B) 1260
(C) 1060
(D) 1160
(E) 1460
a: Stream of consciousness: There are 36 students and every one has equal chance of being selected as a leader. Hence, the leader can be appointed in 36 ways. When one person is appointed as leader, we are left with 35 students. Out of these 35 teachers, we can select one class representative. So, a class representative can be selected in 35 ways. Hence, the number of ways in which a leader and class representative can be selected = 36 x 35 = 1260 The answer is (B).

question: A train running at the speed of 60 km/hr crosses a pole in 6 sec. What is the length of the train?
Options:
(A) 356
(B) 278
(C) 127
(D) 100
(E) 150
answer: Stream of consciousness: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 6 = 100 m The answer is (D).

question: If six persons sit in a row, then the probability that three particular persons are always together is -.
Options:
(A) 1/5
(B) 1/7
(C) 1/9
(D) 1/2
(E) 2/7
answer:
Stream of consciousness: 3!4! Required probability = 3!4!/6! = 1/5 The answer is (A).