GATE Questions

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Let the third proportion to 9 & 12 be 'x'.

=> 9:12 = 12 :p

=> p = 12x12/9 = 16.

Here the series of the form is x2 - 1, x2 - 2, x2 - 3,...

 53 x 2 - 4 = 106 - 4 = 102

To rotate is to energy to stop is to inertia. From the definition itself we know that inertia is a property by virtue of which a body continues to be in the state of rest or in state of motion. So over here whenever energy is supplied then the body starts to move that is a displacement is there and it is rotating where as whenever the body is stopped an inertia of rest is created.

So, Rotate : Energy :: Stop : Inertia.

From the given information, the sitting arrangement can be

 P-Q-W-S-U-V-T-R  i.e. in circular as

From the above figure it is clear that opposite to U is P.

M x T / W = Constant
where, M= Men (no. of men)
T= Time taken
W= Work load
So, here we apply
M1 x T1/ W1 = M2 x T2 / W2
Given that, M1 = 4 men, T1 = 7 hours ; T2 = 2 hours, we have to find M2 =?
Note that here, W1 = W2 = 1 road, ie. equal work load.
Clearly, substituting in the above equation we get, M2 = 14 men.

The Eastern Ghats are a discontinuous range of mountains along India's eastern coast whereas Western Ghats also known as Sahyadri is a mountain range that runs parallel to the western coast of the Indian peninsula.

Eastern ghats and Western ghats meet at the Nilgiri hills in Tamilnadu.

SP of first article = Rs.1000

Profit = 20%

 CP = SP x 100100+P% = Rs. 25003

SP of Second Article = Rs.1000

 Loss = 20%

 CP = SP x 100100-L% = Rs. 1250

So, Total SP = Rs.2000; Total CP = Rs.6250/3

As the CP is more than SP, he makes a loss.

Loss = CP - SP = (6250/3) - 2000 = Rs.(250/3)

So, Loss Percent = Lossx100/CP = 4%

The ratio of A & B investments = (3x8 + 2x4):(4x8 + 5x4)

=> 8:13

=> 8/21 x 630 = 240.