Explanation

Given:

Average = 18

Numbers: 7, 13, 17, x, 29

Average = (Sum of numbers) / (Total count)

18 = (7 + 13 + 17 + x + 29) / 5

Multiply both sides by 5:

90 = 66 + x

x = 90 - 66

x = 24

Explanation

Given x + 1/x = 5

To find x² + 1/x²:

(x + 1/x)² = x² + 2(x)(1/x) + 1/x²

= x² + 2 + 1/x²

x² + 1/x² = (x + 1/x)² - 2

= 5² - 2

= 25 - 2

= 23

Explanation

Population in 2020 = 50,000

Growth rate = 8%

Increase = 8% of 50,000

= 0.08 × 50,000

= 4,000

Population in 2021 = 50,000 + 4,000

= 54,000

Explanation

We can simplify the expression using the identity:  

a³ + b³ = (a + b)(a² - ab + b²)

Here,  

a = 8.73, b = 4.27  

a + b = 13  

a² = 8.73² = 76.2129  

b² = 4.27² = 18.2329  

ab = 8.73 × 4.27 = 37.2671  

Now,  

a³ + b³ = (13)(76.2129 - 37.2671 + 18.2329)  

= 13 × (57.1787)  

≈ 743.3

Explanation

 We are given:

Average of 6 numbers = 10

So, total sum = 10 × 6 = 60

If each number is multiplied by 3, then the new total becomes:

New total = 60 × 3 = 180

Number of values = still 6

New average = 180 ÷ 6 = 30

Explanation

We are given:

• Average age of 3 people = 25

• So, total age = 25 × 3 = 75

Their ages are in the ratio 3:5:7, which means:

Let their ages be 3x, 5x, and 7x

• Total = 3x + 5x + 7x = 15x

Set 15x = 75
⇒ x = 5

So, the ages are:

• 3x = 15

• 5x = 25

• 7x = 35

The lowest age is 15

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

Given:

a : b : c = 2 : 5 (let's assume a common multiple for b and c to match both ratios)

b : c = 3 : 7

To match both ratios, let's find the LCM for b in both ratios.

Given a : b = 2 : 5 and b : c = 3 : 7, let's make the ratios comparable by finding a common multiple for b.

For a : b = 2 : 5 and b : c = 3 : 7,

let's scale a : b : c = 2_3 : 5_3 : 5*7 = 6 : 15 : 35

Now b : c = 15 : 35 which simplifies to 3 : 7.

Given a : b : c = 6 : 15 : 35

a : c = 6 : 35

Explanation

First, calculate the total sum: average × 5

Then subtract the marks of the student who left, and divide the result by 4 to get the new average.

Explanation

Let's denote the cost price as CP.

Given selling price (SP) = Rs 2400

Loss percentage = 20%

CP = SP / (1 - Loss percentage)

= 2400 / (1 - 0.20)

= 2400 / 0.80

= Rs 3000