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Given total 16 Red roses and 14 White roses = 30 roses

Four flowers have to be selected from 30 i.e,  C430= 27405 Ways 

Now, atleast one Red rose is selected i.e, 27405(total) - 1(all four are white roses)  = 27404 ways. 

Distance to be covered = πD = 40π km 

Relative speed of bikers = 16 + 14 = 30 kmph.

Now, time=distancespeed =  40π30 = 4.18 hrs.

Let us assume Amount be 100 Rs and we calculate in CI

 First year 60% of 100 = 60 amount (100+60) is 160

 Second year 60% of 160 = 96 amount (160+96) is 256

 Third year 60% of 256 =153.6 amount (256+153.6) is 409.6

 Here the Amount of 100 Rs is quadrapled in 3 years.

 One year contains 2 half years

 Three year has 6 half years.

 Therefore,  It takes 6 half years.

Let the cost price be x and selling price be y.
Loss = x – y

When the cost price doubles, the loss gets tripled.
So it becomes like this, 2x – y = 3(x-y)

=> x = 2y

Loss % = (loss/ C.P) x 100 = [(2y-y)/2y] x 100= 50 %

Given that, 4198+612345+34866+2411+1

Now Power Cycle of

4 is 4, 6 

6 is 6 

8 is 8, 4, 2, 6

1 is 1

4198- 198 is even number , So the unit digit value is 6 

612345 - It is always 6

34866-  66/4 the remainder is 2 , So the second value is 4

2411- 11 is odd number, So the unit digit value is 4

1 - It is always 1 

Total = 21

Therefore, The unit digit is 1

Gold coins = 18000 , Silver coins = 9600 , Bronze coins = 3600

Find a number which exactly divide all these numbers 

That is HCF of 18000, 9600& 3600 

All the value has 00 at end so the factor will also have 00.

HCF for 180, 96 & 36.

Factors of  

180 = 3 x 3 x 5 x 2 x 2

96 = 2 x 2 x 2 x 2 x 2 x 3 

36 = 2 x 2 x 3 x 3 

Common factors are 2x2×3=12

 Therefore, Actual HCF is 1200

Gold Coins 18000/1200 will be in 15 rooms

Silver Coins 9600/1200 will be in 8 rooms

Bronze Coins 3600/1200 will be in 3 rooms

Total rooms will be (15+8+3)  =  26 rooms.

Given the ratio of the circumference of front wheel  is 40 inches and back wheel is 70 inches. 

Distance covered = Circumference of the wheel × No. of Revolutions made by the wheel

If n is the number of revolutions made by back wheel, the number of revolutions made by front wheel is n+15

Distance covered by both the wheels is the same

i.e, 40*(n+15)=70n

 n=20 

                Front wheel      :      Back Wheel 

 Circumference       40      :      70 

 Revolutions           35      :      20

Distance covered  :  40×35 = 70×20 = 1400 inches.

"Censure" means expressing formal disapproval. "Enthral" means spellbound or enchant, which is farthest in meaning to the given word.