Quantitative Aptitude - Arithmetic Ability Questions

Let the 1 day work of a boy=b and a girl=g, then
2b + g = 1/5 ---(i) and
b + 2g = 1/6 ---(ii)
On solving (i) & (ii), b=7/90, g=2/45
As payment of work will be in proportion to capacity of work and a boy is paid $ 28/week,
so a girl will be paid 28×245790 = 16 $.

(16M + 12W) x 20 = 18W x 40

=> 2M = 3W

Then,
Convert all men into women

12M + 27W = 27 + 12 x 3/2W = 45W

Let number of days required be 'D'

=> 18 x 40 = 45 x D

=> D = 16 days.

Let x = the youngest child. Each of the other four children will then be x+3, x+6, x+9, x+12. 

We know that the sum of their ages is 50 .

so, x+(x+3)+(x+6)+(x+9)+(x+12) = 50

=>  x= 4

 The youngest child is 4 years old.

Let the required number of bottles be x.

More weavers, More mats (Direct Proportion)

More days, More mats (Direct Proportion)

$$\begin{gathered} weavers 4:8} :4:x \\ days 4:8}:4:x \end{gathered}$$ 

4 x 4 x x = 8 x 8 x 4

=> x = 8*8*44*4

=> x = 16.

Given S = 17 yrs

A = 16 yrs

B = 12 yrs

Average = 17 + 16 + 12/3 = 15 yrs

Given if Aslam added to them, their average increases by 5

=> Average of 4 members = 20

Let the age of Aslam be 'x'

Then, 

17 + 16 + 12 + x /4 = 20

=> x = 80 - 45

=> x = 35. 

Hence, the age of Aslam is 35 yrs.

The third proportional of two numbers p and q is defined to be that number r such that

p : q = q : r.

Here, required third proportional of 10 & 20, and let it be 'a'

=> 10 : 20 = 20 : a

10a = 20 x 20

=> a = 40

Hence, third proportional of 10 & 20 is 40.

To get the solution that contains 1 part of milk and two parts of water,
they must be mixed in the ratio as
7x+6x/5y+11y = 1/2
26x = 16y
x/y = 16/26
x/y = 8/13

a2b2=225/256