GATE Questions

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Let the Cost price of the powerbank = Rs. P

But given that by selling it at Rs. 1950, it gives a loss of 25%

=> P x 75100 = 1950
=>P = 1950 x 10075 = Rs. 2600
Now, to get a profit of 25%

Selling Price = 2600 x 125100 = Rs. 3250.

As we know that Speed = Distance / Time
for average speed = Total Distance / Total Time Taken
Thus, Total Distance = 325 + 470 = 795 km
Thus, Total Speed = 7.5 hrs
Average Speed = 795/7.5 => 106 kmph.

Let number of pages in a book = p

According to questions

p - [3p/7 + (2/5 x 4p/7)] = 36

= p - 23p/35 = 36

=> 12p = 36 × 35

p = 105

Here in the given number puzzle, the given numbers follows a pattern that 

1 + 4 = 5 => 1 x 4 + 1 = 4 + 1 = 5 

2 + 5 = 12 => 2 x 5 + 2 = 10 + 2 = 12   

3 + 6 = 21 => 3 x 6 + 3 = 18 + 3 = 21 

Similarly, 

8 + 11 = 96 => 8 x 11 + 8 = 88 + 8 = 96  

Hence, the missing number in the given number puzzle is 96.

Given a jeep travels a certain distance taking 6 hrs in forward journey
During the return journey, it takes 4 hrs with an increased speed 12 km/hr
Let 'x' be the distance.
Now, speed is given by distance/time.
Here the difference between both speeds = 12

 x4 - x6 = 12

 3x - 2x12 = 12

=> x = 144 km

Therefore, the distance travelled by the jeep in forward or return journey is x = 144 km.

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.

Let the required Sum = Rs.S

 From the given data,

 1008 = [(S x 11 x 5)/100] - [(S x 8 x 6)/100]

 => S = Rs. 14,400.

Total number of letters in the word ABYSMAL are 7

Number of ways these 7 letters can be arranged are 7! ways

But the letter is repeated and this can be arranged in 2! ways

Total number of ways arranging ABYSMAL = 7!/2! = 5040/2 = 2520 ways.