GATE Questions

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Between the two I prefer tea is the correct sentence with suitable preposition.

Let the speeds of the two trains be x m/sec and y m/sec respectively.

Then, length of the first train = 27 x meters, and

length of the second train = 17 y meters.

(27 x + 17 y) / (x + y) = 23

=> 27 x + 17 y = 23 x + 23 y

=> 4 x = 6 y

=> x/y = 3/2.

The third proportional of two numbers p and q is defined to be that number r such that

p : q = q : r.

Here, required third proportional of 10 & 20, and let it be 'a'

=> 10 : 20 = 20 : a

10a = 20 x 20

=> a = 40

Hence, third proportional of 10 & 20 is 40.

Ratio of investments of A, B & C = 2×6+4×6 : 3×12 : 4×12

= 36 : 36 : 48

= 6 : 6 : 8

But given that the annual profit of B is Rs. 3000

=> 6 ratio = 3000

Then for the total annual profit of partners is

20 ratio = 3000 x 20/6 = 10,000.

The path that data takes from source to destination is called a Channel. A channel is a communication medium. A channel has a certain capacity for transmitting information. 

The "capacity" of a channel is the theoretical upper-limit to the bit rate over a given channel that will result in negligible errors. Channel capacity is often measured by its Bandwidth in Hz or its data rate in bits per second.

Say total cost price of tea is x.
Then total profit at a rate of 15% is = (15x/100)
According to question,
15x/100 = 60
so x = 400
C.p of the tea is Rs. 400.
so total selling price will be = (400+60) = Rs.460
so the quantity of the tea will be = (460/5.75) = 80kg.

343 = 73,  1331 = 113 , 2197 = 133, 121 = 112

343, 1331, 2197 are perfect cubes, but not 121.

h =   = 3 × 10⁸/10⁶ = 300 m