GATE Questions

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Let 1 woman's 1 day work = x.

Then, 1 man's 1 day work = x/2 and 1 child's 1 day work  x/4.

So, (3x/2 + 4x + + 6x/4) = 1/7

28x/4 = 1/7 => x = 1/49

1 woman alone can complete the work in 49 days.

So, to complete the work in 7 days, number of women required = 49/7 = 7.

Given number of boxes = 14

Number of workers = 4

Now, number of whole boxes per worker = 14/4 = 3.5 

Hence, number of whole boxes per each coworker = 3

Here Thread and String are Synonyms of each other. Then the answer will be the synonym of Cask. 

• Cask is nothing but a large barrel-like container used for storing liquids, typically alcoholic drinks. 

Ex : Drum, Vessel, Tank, Barrel, Hogshead, Firkin,...

• Here from the options Barrel is the only synonym of Cask.

Thus,  Thread : String :: Cask : Barrel

Let the third proportion to 9 & 12 be 'x'.

=> 9:12 = 12 :p

=> p = 12x12/9 = 16.

Lets say shyam sells at 100,

Since Ram sells 25% cheaper than Shyam,

Therefor Ram sells at less than 25% of100 or 75 rs.

Ram sells 25% dearer than Bram or 125% of Ram =100% of Bram or

125% of x (say x price of bram )=75rs.
or 100% of x =60rs.
hence price of bram is 60rs.

now Bram's good is cheaper than Shyam's as (100-60)x100/100% or 40%.

Hence Brams Good is 40% cheaper than that of Shyam's good.

Here the series of the form is x2 - 1, x2 - 2, x2 - 3,...

 53 x 2 - 4 = 106 - 4 = 102

No. of people who read Hindu = 285
No. of people who read TOI = 127
No. of people who read IE = 212
Now,
No. of people who read Hindu and TOI both is = 20
No. of people who read TOI and IE both is = 35
No. of people who read Hindu and IE both is = 29
Let No. of people who read Hindu , TOI and IE all is = x ;
So, only Hindu is = 285-20-29-x = 236-x ;
Only TOI is = 127-20-35-x = 72-x ;
Only IE is = 212-35-29-x = 148-x ;
Now, 236-x + 72-x + 148-x + 20 + 29 + 35 + x + 50 = 500 590 -2x = 500
So, x = 45 this is the value who read all the 3 dailies.
So, No. of people who read only one paper is = 236-45 + 72-45 + 148-45 = 191 + 27 + 103 = 321.

To rotate is to energy to stop is to inertia. From the definition itself we know that inertia is a property by virtue of which a body continues to be in the state of rest or in state of motion. So over here whenever energy is supplied then the body starts to move that is a displacement is there and it is rotating where as whenever the body is stopped an inertia of rest is created.

So, Rotate : Energy :: Stop : Inertia.