Exams

Here in the given numbers 91 is a Composite number. Since it has factors of 7 and 13 other than 1 and itself.

Composite Numbers :

A composite number is a positive integer which is not prime (i.e., which has factors other than 1 and itself).

Examples :: 4, 6, 8, 12, 14, 15, 18, 20, ...

The work to be done = Capacity of reservoir  = 30 litres.

 1^st Minute ---> inlet pipe opened ---> 5 lit filled

 2^nd minute ---> inlet pipe closed; outlet pipe opened ---> 4 lit emptied

In 2 minutes (5 litres - 4 litres = 1lit) is filled into the reservoir.

It takes 2 minutes to fill 1lit ---> it takes 50 minutes to fill 25 litres into the reservoir.  

In the 51^st minute inlet pipe is opened and the reservoir is filled.

The words in each pair are synonyms. Here Foresight and Anticipation are synonyms to each other and Insomnia is a synonym to Sleeplessness.

Hence, Foresight : Anticipation :: Insomnia : Sleeplessness.

The surface area of a cube = 6a2 =  6 side2

New  Surface area = 6 x 1.44a2

Therefore, 0.44a2a2x100 = 44%

0.127 expressed as a fraction = 127/1000

1/8 can also be expressed as (1 x 125) / (8 x 125) = 125/1000

The difference is 2/1000, which is 1/500

Let the average expenditure per head be Rs. p
Now, the expenditure of the mess for old students is Rs. 44p
After joining of 15 more students, the average expenditure per head is decreased by Rs. 3 => p-3
Here, given the expenditure of the mess for (44+15 = 59) students is increased by Rs. 33
Therefore, 59(p-3) = 44p + 33
59p - 177 = 44p + 33
15p = 210
=> p = 14
Thus, the expenditure of the mess for old students is Rs. 44p = 44 x 14 = Rs. 616.