GATE Questions

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From the given data,

containers contain mixtures of milk and water as 1365 lit, 1560 lit and 1755 lit.

Biggest measure that can measure all these different quantities exactly can be given by

HCF of (1365, 1560, 1755) 

That can be found as 

HCF of 1365, 1755 = 195

Now, HCF of 195 and 1560 = 195

Hence, biggest measure that can measure all the given different quantities exactly is 195 lit.

The U.S. e-commerce giant, Amazon has been awarded a patent for launching a giant flying warehouse that would acts as a launch pad for drones to deliver items within minutes.The patent reveals plans for setting up an “Airborne Fulfillment Center” (AFC) such as an Airship or Blimp, floating at an altitude of around 45,000 and stocked with lots of products especially in area where the demand for certain items is expected to be high. When a customer places an order, a drone or unmanned aerial vehicles (UAV) will fly down and deliver the package. The patent claims that this would require little or no power because the drone would be gliding down rather than having to take off and land.

Given,
S.I = 3 Principal Amount
=> 3A = A x 16 x R/100
By solving, we get
=> R = 18.75%

Let the actual distance be t kms

Now, According to the data,

$$\begin{gathered} 5t + 860 = 6t \\ => 560t + 860 = 6t \\ => 60t + 8 = 72t \\ => 8 = 12t \\ => t = 8/12 = 2/3 hrs \end{gathered}$$

Now, the total distance = 6t = 6 x 2/3 = 2 x 2 = 4 kms.

From the given data,

3500x7xt/100 = 500

=> t = 100/49 years

Now, in the second case

The interest per year = 49/100 x 800 = 392

 => 4900 x 1 x r/100 = 392

=> r = 8%

Investments ratio is = 3:1
Time period ratio is = 2:1

As they are proportional to gain

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Gain ratio of Vishal and raghu = 6:1

But given Raghu got Rs. 4000, 

=? 1 ----- 4000
     7 -----    ?

=> Rs.28,000

The total gain = Rs.28,000

Number of pages typed by Adam in 1 hour = 36/6 = 6
Number of pages typed by Smith in 1 hour = 40/5 = 8
Number of pages typed by both in 1 hour = (6 + 8) = 14
Time taken by both to type 110 pages = (120 * 1/14) = 847 = 8 hrs 34 min.