In what time will a railway train 50 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
(A) 5 sec
(B) 4 sec
(C) 3 sec
(D) 6 sec
(E) 1 sec

T = 50/36 * 18/5 = 5 sec So the answer is: (A).

A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 3 days. In how many days can they complete the remaining work?
Options:
(A) 4/3 days
(B) 2 days
(C) 8 days
(D) 3 days
(E) 9 days

Work done by A in 3 days = 3/5
Remaining work = 2/5
Work done by both A and B in one day = 1/5 + 1/10 = 3/10
Remaining work = 2/5 * 10/3 = 4/3 days. So the answer is: (A).

Every Sunday, Giri jogs 3 miles. For the rest of the week, each day he jogs 1 mile more than the previous day. How many miles does giri jog in 2 weeks ?
Options:
(A) 42
(B) 63
(C) 84
(D) 98
(E) 108

In one week, Giri jogs 3 + 4 + 5 + 6 + 7 + 8 + 9 = 42 miles
In two weeks, Giri jogs 84 miles. So the answer is: (C).

Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:
Options:
(A) 9 minutes
(B) 7
(C) 6
(D) 5
(E) 4

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
Let B be turned off after x minutes. Then, Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1. x(2/75 + 1/45) + (30 - x). 2/75 = 1 11x/225 + (60 - 2x)/75 = 1 11x + 180 - 6x = 225. x = 9. So the answer is: (A).