Explanation

Let the number be x.

Two-third of the number is (2/3)x.

The problem states that multiplying the number by two-third of itself gives 864, so we can set up the equation: x × (2/3)x = 864.

Simplifying the equation, we get: (2/3)x² = 864.

Multiplying both sides by 3/2, we get: x² = 864 × (3/2) = 1296.

Taking the square root of both sides, we get: x = √1296 = 36.

So, the correct answer is: 36

Explanation

We are selecting three different posts here, so order matters.

Thus, total ways of selecting a President, VP and Water-boy from a group of 10 people would be 10P3.

Explanation

Means x = 5, y = 2

Putting value of x and y in expression

8 × 5 + 9 × 2 = 58

8 × 5 + 2 × 2 = 44

58 : 44 = 29 : 22

Explanation

1. 10^0.48 = x

2. 10^0.70 = y

3. x^z = y^2

We can rewrite the third equation as:

(10^0.48)^z = (10^0.70)^2

Using the power rule of exponents:

10^0.48z = 10^1.40

Since the bases are the same (both are 10), we can equate the exponents:

0.48z = 1.40

Now, divide both sides by 0.48:

z ≈ 1.40 / 0.48

z ≈ 2.92

So, the value of z is closest to 2.9.

Explanation

To find the answer, divide 4.036 by 0.04:

4.036 ÷ 0.04 = 100.9

Explanation

A/B = 2/3

B/C = 3/4

A/D = 4/5

We can start by finding the relationship between B and D:

B/A = 3/2 (inverse of A/B)

A/D = 4/5

Multiplying these two fractions, we get:

B/D = (3/2) × (4/5) = 12/10 = 6/5

Now, we can find C/D:

C/D = (C/B) × (B/D)

= (4/3) × (6/5)

= 8/5

Explanation

In this scenario, we can use the tangent function, which is the ratio of the opposite side (height of the tower, h) to the adjacent side (the horizontal distance, 70m):

Explanation

A : B = 2 : 3

B : C = 4 : 5

Calculation :

A : B = 2 : 3 ---- (1) × 4

B : C = 4 : 5 ---- (2) × 3

Multiply by 4 in equation (1) and multiply by 3 in equation (2)

∴ A : B : C = 8 : 12 : 15

Explanation

Let's assume the cost of the bike is x. Then, the cost of the car is 400% greater than the cost of the bike, which means the cost of the car is x + 400% of x = x + 4x = 5x.

The total cost of 5 cars and 10 bikes is:

5(5x) + 10x = 25x + 10x = 35x

The increase in cost is:

5 cars: 15% of 5(5x) = 0.15(25x) = 3.75x

10 bikes: 20% of 10x = 0.20(10x) = 2x

Total increase = 3.75x + 2x = 5.75x

The percentage increase is:

(5.75x / 35x) × 100 = (575 / 3500) × 100 = 16 3/7%

Explanation

Initially, the average of five numbers is 27, so the sum of these five numbers is:

5 x 27 = 135

If one number is excluded, the average becomes 25, which means the sum of the remaining four numbers is:

4 x 25 = 100

Now, let's find the excluded number by subtracting the sum of the remaining four numbers from the initial sum:

135 - 100 = 35

So, the excluded number is 35.