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Given that 

6 men and 8 boys can do a piece of work in 10 days 

26 men and 48 boys can do the same in 2 days

As the work done is equal,

10(6M + 8B) = 2(26M + 48B)

60M + 80B = 52M + 96B

=> M = 2B

=> B = M/2 ……(1)

Now Put (1) in 15M + 20B

=> 15M + 10M = 25M

Now, 6M + 8B in 10 days

=> (6M + 4M) 10 = 100M

Then D(25M) = 100M

=> D = 4 days.

The given number series is  21 56 102 160 231 316

21      56       102        160      231       316         416

   +35    +46       +58       +71      +85       +100

        +11      +12       +13      +14      +15

Hence, the next number in the given number series is 316 + 100 = 416.

Let the numbers be 3x, 3x + 3 and 3x + 6.
Then,
3x + (3x + 3) + (3x + 6) = 72
9x = 63
x = 7
Largest number = 3x + 6 = 27.

=> Second largest number = 27 - 3 = 24

Here E = 5 = 5/1 = 5

=> READ = 18 + 5 + 1 + 4 = 28/4 = 7

=> DEAR = 4 + 5 + 1 + 18 = 28/4 = 7

125 over 1000 in Simplest Form means 1251000 in its simple fraction form.

Now, to get the simplest form of 125/1000, find the HCF or GCD of both numerator and denominator i.e, 125 and 1000.

HCF of 125, 1000 = 125

Then, divide both numerator and denominator by 125

i.e, 1251251000125 = 18

Hence, 18 is the simplest form of 125 over 1000.

The given number series 9, 19, 21, 43, 45, ... follows a pattern that

ALternately (x 2 + 1) and  (x 1 + 2)

9 

9 x 2 + 1 = 19

19 x 1 + 2 = 21

21 x 2 + 1 = 43

43 x 1 + 2 = 45

45 x 2 + 1 = 91

Hence, the next number in the given sequence is 91.

             A              :               B
(8000x4)+(4000x8) : (9000x6)+(6000x6)
         64000           :      90000
=>        32 : 45