Aptitude and Reasoning Questions

Work done by P alone in one day = 1/6th of the total work done by Q alone in one day = 1/3(of that done by P in one day) = 1/3(1/6 of the total) = 1/18 of the total. 

Work done by P and Q, working together in one day = 1/6 + 1/18  = 4/18 = 2/9 

They would take 9/2 days = 4 (1/2) days to complete the work working together.

we can do this by trial and error method.

Putting x = 2,we get 2²(2² - 1) = 12.
checking with other integers, the above equation always gives a value which is a multiple of 12,
So, x²(x² - 1) is always divisible by 12.

Q, the Doctor, is the father of T. S, the Housewife, is the grandmother of T and hence the mother of Q. Since there are only two married couples one being that of Q, the grandfather of R. i.e, U must be married to S. Thus, R and T will be both children of Q and these must be the students So, P, who remains, shall be the wife of Q and she alone can be the nurse. Thus, U must be the contractor 

Clearly, for definite the males are Q, the father and U, the grandfather 

When in winter, hot water is poured in the glass tumbler. its inner surface tends to expand while the Outer surface in contact with cold atmosphere does not. This opposite interaction causes the tumbler to break. 

From the given information in the question
24 ÷ 4 + 6 - 3 x 4
6 + 6 - 12 = 0

Given total sum = Rs. 427
And given that 3 times A’s share, 4 times B’s share and 7 times C’s share are all equal.
=> 3A = 4B = 7C
But given
=> A + B + C = 427
Now express A and B in terms of C i.e
=> (7C/3) + (7C/4) + C = 427
=> C = 84