GATE Questions

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From a container of wine, a thief has stolen 15 litres of wine and replaced it with same quantity of water. He again repeated the same process. Thus, in three attempts the ratio of wine and water became 343 : 169. The initial amount of wine in the container was:

Given that 10^0.48 = x,  10^0.70 = y and x^z = y²,  then the value of z is close to ___ ?

Hemavathi gets 3 marks for each right sum and loses 2 marks for each wrong sum. He attempts 35 sums and obtains 60 marks. The number of sums attempted correctly is ?

A train covered k km at 40 kmph and another 2k km at 20 kmph. Find the average speed of the train in covering the entire 3k km ?

In what time will Rs. 3300 becomes Rs. 3399 at 6% per annum interest compounded half-yearly ?

If Hema walks at 12 km/hr instead of 8 km/hr, she would have walked 20 km more. The actual distance travelled by Hema is ?

A word arrangement machine, When given an input line of words, rearranges it in every step following a certain rule. Following is an illustration of an input line of words and various steps of rearrangement.

Input: gone are take enough brought station
Step 1: take gone are enough brought station
Step 2: take are gone enough brought station
Step 3: take are station gone enough brought
Step 4: take are station brought gone enough
And Step 4 is the last step for this input. Now, find out an appropriate step in the following question following the above rule.

Question:
Input: car on star quick demand fat
What will be the third step for this input ?

On a ruler's tombstone, it is said that one sixth of his life was spent in childhood and one twelfth as a teenager. One seventh of his life passed between the time he became an adult and the time he married; five years later, his son was born. Alas, the son died four years before he did. He lived to be twice as old as his son did. How old did the ruler live to be ?