GATE Questions

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Let number of days Charan can do the same work alone is 'd' days.

According to the given data,

$$\begin{gathered} 512 + 716 + 14d = 1 \\ 14d = 1 - 20 + 2148 \\ 14d = 48 - 4148 \\ d = 14 x 487 \\ d = 96 days \end{gathered}$$

Therefore, Charan alone can complete the work in 96 days.

A pure substance can be defined as any single type of material that has not been contaminated by another substance. In chemistry, a pure substance has a definite composition. It can be a compound or an element. A pure substance is considered to be a material that consists of one type of "building block" of matter.

Examples of pure substances include tin, sulfur, diamond, water, pure sugar (sucrose), table salt (sodium chloride) and baking soda (sodium bicarbonate).

Tin, sulfur, and diamond are examples of pure substances which are chemical elements. All elements are pure substances.

Water, sugar, salt and baking soda are pure substances which are chemical compounds. Chemical compounds also are pure substances

The shadow zone is the area of the earth from angular distances of 104 to 140 degrees from a given earthquake that does not receive any direct P waves. The shadow zone results from S waves being stopped entirely by the liquid core and P waves being bent (refracted) by the liquid core.

There are two types of Shadow zones:

one for P waves and

one for S waves.

P wave shadows between 104-140 degree, both sides; S wave shadow from 105 of one side to 105 of the other.

Fruits reduced by 1/4.
Total no. of bags N = 5
Formula to find no. of fruits in 1st bag = 4^n
Last Bag = 4 fruits.
That means, 4th bag = 4 x 4 = 16 fruits
3rd bag = 16 x 4 = 64 fruits
2nd bag = 64 x 4 = 256 fruits
1st bag = 256 x 4= 1024 fruits.

G.C.D is nothing but H.C.F

Given numbers are 1.08 , 0.36 and 0.90

we can take as 108, 36 and 90 

Then required H.C.F is 18.

Therefore, H.C.F of given numbers is 0.18.

Number of books that can be placed in the larger box is given by Volume of Box / Volume of book.
Now, n = 25 x 42 x 60 / 7 x 6 x 5
= 63000 / 210
= 300.
Therefore, 300 books can be in that box.

Let total amount = Rs. P

Total expenditure = (23 + 33 + 19 + 16)% of P = 91%ofP

Remaining money = (100 - 91)% of P = 9% of P

But given in the question that,

9% of P = 504

9p/100 = 504

=> P = 50400/9

=> P = Rs. 5600

Required money spent on Food & Insurance = 23 + 33 %

= 56% of 5600

= 56 x 5600/100 = 56 x 56 = Rs. 3136