question: A Train requires 10 seconds to pass a pole while it requires 35 seconds to cross a stationary train which is 500 mtrs long. Find the speed of the train.
Options:
(A) 68 kmph
(B) 70 kmph
(C) 72 kmph
(D) 60 kmph
(E) 50 kmph
answer: Stream of consciousness: In 10s the train crosses the pole and in 35 sec the train crosses one more stationary train
In 25 sec the train travels a distance of 500 mtrs
Speed = 500/25 = 20 m/s = 20 (3600/1000) = 20 * 18/5 = 72 kmph The answer is (C).


q: A cricket bat is sold for $900, making a profit of $300. The profit percentage would be
Options:
(A) 24%
(B) 25%
(C) 30%
(D) 50%
(E) 40%
a: Stream of consciousness: 300/(900 - 300) = 50%. The answer is (D).


question: The average of seven numbers is 24. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
Options:
(A) 27
(B) 29
(C) 31
(D) 34
(E) 69
answer: Stream of consciousness: The total of seven numbers = 7X24 = 168
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (168 - 99 ) = 69 The answer is (E).


q: By how much is 50% of 250 greater than 25% of 400.
Options:
(A) 25
(B) 26
(C) 29
(D) 39
(E) 26
a: Stream of consciousness: (50/100) * 250 â€“ (25/100) * 400
125 - 100 = 25 The answer is (B).


question: 30 pens and 75 pencils were purchased for 690. If the average price of a pencil was 2.00, find the average price of a pen.
Options:
(A) 10
(B) 11
(C) 18
(D) 13
(E) 14
answer: Stream of consciousness: Since average price of a pencil = 2
∴ Price of 75 pencils = 150
∴ Price of 30 pens = (690 – 150) = 540
∴ Average price of a pen = 540⁄60 = 18 The answer is (C).


question: If six persons sit in a row, then the probability that three particular persons are always together is ?
Options:
(A) 1/6
(B) 1/0
(C) 1/5
(D) 1/4
(E) 1/1
answer:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
Stream of consciousness: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5 The answer is (C).