GATE Questions

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Let the distance traveled be x km.
Then, x/10 - x/15 = 2
3x - 2x = 60 => x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60/10 = 6 hrs.
So, Robert started 6 hours before 2. p.m. i.e., at 8 a.m.
Required speed = 60/5 = 12 kmph.

Initial wheat per kg cost be Rs. 100

Then, monthly expenditure of the family = 30 x 100 = 3000

After increase in cost,

Let P be new monthly consumption of family.

P x 132 = 110/100 x 3000

=> P = 25 kg.

Let Cost Price(C.P) = P
gain% = {(S.P-C.P)/C.P} x 100
25 = {(1540-P)/P} x 100
25/100 = (1540-P)/P
=> P = 4(1540)-4P
=> 5P = 4(1540)
=> P = 1232
So, Cost Price = Rs. 1232

Clearly, we may mark such sets of 3 numbers, in which the middle number is 8 and each of the two numbers on both sides of it is a factor of 8, as shown below :

2 8 3 8 2 4 8 2 4 8 6 8 2 8 2 4 8 3 8 2 8 6

So, there are two such 8's. Hence the answer is C.

Since level of water increased in cylinder by height 4. 

This is because of the rectangular block .

Therefore , area of rectangular block immersed in water is 

= 227×6×6×4  

Thats why portion of block immersed in water is 

= (22/7 * 36 * 4) / total vol. of rectangle 

= (22/7 * 36 * 4)/ (7*5*6) 

= (22/7 * 24)/ 35.

Time taken to meet the first time = length of track/relative speed

Given the length of the track is 600 m

The relative speed = 25 + 35 = 60 kmph = 60 x 5/18 m

Therefore Time = 60025+35518= 600/60 x (18/5) = 36 sec.

The opposite of right is left. The opposite of left is take. And the opposite of take is give.

Hence, the opposite of right is the opposite of take which is left.

Distance travelled by Ramu = 45 x 4 = 180 km

Somu travelled the same distance in 6 hours.

His speed = 180/6 = 30 km/hr

Hence in the conditional case, Ramu's speed = 45 - 9 = 36 km/hr and Somu's speed = 30 + 10 = 40km/hr.

Therefore travel time of Ramu and Somu would be 5 hours and 4.5 hours respectively.

Hence difference in the time taken = 0.5 hours = 30 minutes.