Quantitative Aptitude - Arithmetic Ability Questions

We know that, 

The area of a triangle with two sides given and included angle

A = 1/2 x product of sides x Sin(angle) 

Here the two sides are 8 & 12

Angle = 150

Area = 1/2 x 8 x 12 x sin150

Sin(150) = sin(90+60) = cos(60) = 1/2

A = 48 x 1/2 = 24

Area of the given triangle = 24 sq units.

$$\begin{gathered} 78 x 448 + 67 x 3374 \\ => 392 + 2892 \\ => 3284 \end{gathered}$$

(300 – 101)/11 = 199/11 = 18 1/11

18 Numbers.

Let the present ages of the mother and daughter be 2x and x years respectively.
Then, (2x - 18) = 3(x - 18) => x = 36
Required sum = (2x + x) = 108 years.

Given word is SCOOTY

ATQ,

Except S & Y number of letters are 4(C 2O's T)

Hence, required number of arrangements = 4!/2! x 2! = 4!

= 4 x 3 x 2

= 24 ways.

Using Pythagoras theorem we can see that 12² + 15² is not equal to 18²
Neither is 10² + 24² = 25²

Given that to find 15 of 80

=> What % of 80 is 15

Let it be 'p'

=> p% of 80 = 15

=> $$\begin{gathered} p x 80100 = 15 \\ ⇒p = 15 x 10080 \\ ⇒p = 150080 = 18.75 \end{gathered}$$

Therefore, 15 is 18.75% of 80 => 18.75% of 80 = 15

Example::

Now, in the similar way we can find 15% of 80 =?

=> 15x80/100 = p

=> p = 4 x 3 = 12

Therefore, 15% of 80 = 12