Explanation

x + 1/x = 15

(x + 1/x)² = 15²

x² + 2(x)(1/x) + 1/x² = 225

x² + 2 + 1/x² = 225

x² + 1/x² = 225 - 2

x² + 1/x² = 223

Explanation

A surd is an irrational root.

√16 = 4 (rational)

√25 = 5 (rational)

√16 + √25 = 4 + 5 = 9 (rational)

√21 is irrational, so it's a surd.

Explanation

Given x:y = 3:4 and y:z = 2:5.

To find x:z, we need to make y's ratio the same in both.

y:z = 2:5 = 4:10 (multiply both parts by 2)

Now, x:y = 3:4 and y:z = 4:10

So, x:z = 3:10.

Explanation

The mean of the first five natural numbers (1, 2, 3, 4, 5) is 3

Calculated by summing the numbers (1 + 2 + 3 + 4 + 5 = 15) and dividing by the count of numbers (5). 

Explanation

0.13 × P² = 13

Solve for P²:

P² = 13 / 0.13 = 100

Now take the square root:

P = √100 = 10

Explanation

2A = 3B = 4C

Let k = 2A = 3B = 4C

Now solve for A, B, and C:

- A = k / 2  

- B = k / 3  

- C = k / 4

Now take the ratio A : B : C:

= (k/2) : (k/3) : (k/4)

Multiply all terms by 12 to eliminate denominators: = 6 : 4 : 3

Explanation

Number of boys present: 50% of 100 = 0.5 x 100 = 50 boys

Number of girls present: 40% of 900 = 0.4 x 900 = 360 girls

Total students present = Boys present + Girls present

= 50 + 360

= 410

Now, let's find the percentage of students present:

Total students = Boys + Girls = 100 + 900 = 1000

Percentage of students present = (Total students present / Total students) x 100

= (410 / 1000) x 100

= 41%

Explanation

We are told:

• Arrival time = 15:06 (i.e., 3:06 PM)

• Journey duration = 5¼ hours = 5 hours 15 minutes

Step 1: Subtract 5 hours 15 minutes from 15:06

Start with 15:06

• Subtract 5 hours → 10:06

• Subtract 15 minutes → 9:51

Explanation

Step 1: Find the perimeter of the square

$$\text{Perimeter}=4\times \text{side}=4\times 50=200\text{ meters}$$

Step 2: Calculate total fencing cost

$$\text{Cost}=200\times 8=\text{Rs. }1600$$

Explanation

Equating the two expressions and simplifying gives:

$$x cdot 200 = y cdot 250 Rightarrow frac{y}{x} = frac{200}{250} = frac{4}{5} Rightarrow y : x = 4 : 5$$

⇒y​/x=200/250

=4​/5

⇒y:x=4:5