GATE Questions

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Euclid of Alexandria was a Greek mathematician, often referred to as the Father of Geometry.

        GM    GM
A ---- B ---- E
         |
         |
         C
         |
         |
         D (Grand son or daughter)

Ans. 
Time taken by A to complete a work alone - 24 days
Time taken by A in completing 1/3 of work = 24*1/3= 8 Days
8 day = time taken by B in completing 1/2 of work
B alone can complete the work = 16 days
The required time in completing the work if both A & B start working together?
16*24 / 40 = 48/5 Days

Let the number of males be 'M'
Let the number of females be 'F'
From the given conditions,
(F-15)=2M.....(i)
F=5(M-45).....(ii)
By solving the equations (1) & (2) we get M = 80
Then substitute M = 80 in (1)
F = 2M + 15
F = 2 x 80 + 15
=> F = 175
Therefore, number of males = 80 and females = 175 in the party.

The distance around a shape or figure I called Perimeter. A perimeter is a path that surrounds a two-dimensional shape.

Given Loss = Rs. 40.4
We know loss = cost price - selling price
40.4 = CP - 35(15)
=> CP = 40.4 + 525
=> CP = Rs. 565.4
Now the New selling price of waffer is Rs. 18
=> SP = 35(18) = 630
Now Gain = SP - CP = 630 -565.4 = Rs. 64.6.

The Length of the Day is determined in Astronomical Units.

The length of a day corresponds to the time the Earth takes to turn around on its axis, which is approximately 24 hours. But it's not exactly 24 hours. 

This phenomenon is due to tides raised by the Moon which slow Earth's rotation. Because of the way the second is defined, the mean length of a day is now about 86 400.002 seconds, and is increasing by about 1.7 milliseconds per century.