Exams

Let the initial speed of Akhil be '4p' kmph

Then speed after decrease in speed = '3p' kmph

We know that, 

Change in speed == Change in time

According to the given data,

$$\begin{gathered} 243p - 244p = 35 - 2560 \\ => p = 12 \end{gathered}$$

Hence, the initial speed of Akhil = 4p = 4 x 12 = 48 kmph.

I=Prt

I=12

Balance = P +Prt

412

Find the balance at the end of the second year.

I = Prt=12.36

Balance =P + Prt

424.36

1 2 3 4 5 6(Shankar) 7(Nitu) 8(Althaf) 9 10 11 12 13 14
Here, Althaf is 8th from front, Shankar is 9th from rear end and Nitu is between them
So minimum no. of boys standing in the queue = 14

Let 'x' be the number of new Rs.2000 notes.

Given for one new 2000 note there are three old 500 notes.

i.e, 3x

Given 10 more new Rs.2000 notes are added to the collection
and the ratio of new Rs.2000 notes to old Rs.500 notes 

x+103x=12⇒x=20

Therefore, number of new Rs.2000 notes =  x+10 = 30.

old Rs.500 notes = 3x = 60.

Thus, the total number of notes in the collection  = 30 + 60 = 90.

Here in the given number puzzle, the given numbers follows a pattern that 

1 + 4 = 5 => 1 x 4 + 1 = 4 + 1 = 5 

2 + 5 = 12 => 2 x 5 + 2 = 10 + 2 = 12   

3 + 6 = 21 => 3 x 6 + 3 = 18 + 3 = 21 

Similarly, 

8 + 11 = 96 => 8 x 11 + 8 = 88 + 8 = 96  

Hence, the missing number in the given number puzzle is 96.

End of first year     :  10000 x (3/5) = Rs. 6000
End of second year :  6000 x (3/5) = Rs. 3600
End of third year    :  3600 x (3/5) = Rs. 2160

Number of white marbles = 4

Number of Black marbles = 5

Total number of marbles = 9

Number of ways, two marbles picked randomly = 9C2

Now, the required probability of picked marbles are to be of same color = 4C2/9C2  +  5C2/9C2

= 1/6 + 5/18

= 4/9.