Simplification Questions

Let the number of males be 'M'
Let the number of females be 'F'
From the given conditions,
(F-15)=2M.....(i)
F=5(M-45).....(ii)
By solving the equations (1) & (2) we get M = 80
Then substitute M = 80 in (1)
F = 2M + 15
F = 2 x 80 + 15
=> F = 175
Therefore, number of males = 80 and females = 175 in the party.

(4a+7b)(4c-7d) = (4a-7b)(4c+7d)

(4a+7b)/(4a-7b) = (4c+7d)/(4c-7d)

Using componendo and dividendo

(4a+7b)+(4a-7b) / (4a+7b)-(4a-7b)

= (4c+7d)+(4c-7d) / (4c+7d)-(4c-7d)

Or 8a/14b = 8c/14d

Or a/b = c/d

The given equation is in Mixed fraction.

Now to solve this type of fractions,

$$\begin{gathered} 413 + 215 + 414 =? \\ ? = 4 + 2 + 4 + 13 + 15 + 14 \\ ? = 10 + 4760 \\ ? = 104760 \\ \end{gathered}$$

64/12 = 16/3 in simplest form.

Let the side of regular hexagon be ‘a’

Let height of the tower 1 be h1 and tower 2 be h2

Height of tower 1 = h1 = (distance between A and B)* (tan 30o)= a.1/√3

Distance between A and C = 2*√3.a/2= √3a

Height of tower 2 = h2 = (distance between A and C)* (tan 45o) = √3a.1 = √3a

Ratio of height of towers at B and C respectively =a/√3/√3a = 1/3.

The given inequality is 3p - 16 < 20

For solving this inequality, follow these steps

Now add 16 on both sides

we get 3p - 16 + 16 < 20 + 16

=> 3p  < 36

Now divide the above eqn with 3 on both sides

we get, 3p/3 < 36/3

p < 12.

x : y = 8 : 15
If y = 10, x = 8/15 X 10
y = 16/3

Using BODMAS Rule,

First solve division, mutiplication and Addition

So here 10/2 = 5

Then 2 x 5 =  10

Now, 5 + 10 = 15.

Hence, 5 + 2 x 10/2 = 15.