Explanation

5, _, _, _, 25

There are 5 terms. Let's find the common difference:

d = 25-5/4 = 20/4 = 5

The sequence is:

5 + 5 = 10

10 + 5 = 15

15 + 5 = 20

20 + 5 = 25

The sequence is 5, 10, 15, 20, 25

The second arithmetic mean is 15.

Explanation

To find the Arithmetic Mean (Average):

Add the numbers: 10 + 20 + 30 + 40 + 50 = 150

Count the numbers: 5

Divide the sum by the count: 150/5 = 30

Explanation

If mango juice is 20%, then apple juice is 80% (since 100% – 20% = 80%).

The ratio of mango to apple juice is 20:80, which simplifies to 1:4.

Explanation

Let's assume 2/3 A = 3/4 B = 0.6C = 18

2/3 A = 18 ⇒ A = 27

3/4 B = 18 ⇒ B = 24

0.6C = 18 ⇒ C = 30

A:B:C = 27:24:30 = 9:8:10

Explanation

Given a : b : c = 3 : 4 : 7.

Let's find (a + b + c) : c or any other single term. Here we find (a + b + c) : a

a + b + c = 3 + 4 + 7 = 14

(a + b + c) : a = 14 : 3

Explanation

Let's denote the number of coins as 2x, 3x, and 4x for Rs 2, Rs 5, and Rs 10 coins, respectively.

The total value is:

2(2x) + 5(3x) + 10(4x) = 472

4x + 15x + 40x = 472

59x = 472

x = 8

Number of Rs 2 coins = 2x = 2(8) = 16

Explanation

Given sum of roots = 55 and product of roots = 66.

The quadratic equation is:

x² - (sum of roots)x + (product of roots) = 0

x² - 55x + 66 = 0

Explanation

Let son's current age be x and father's current age be y.

x + y = 70 ... (1)

Three years ago,

son's age = x - 3

father's age = y - 3

Given y - 3 = 3(x - 3)

y - 3 = 3x - 9

y = 3x - 6 ... (2)

Putting (2) in (1):

x + 3x - 6 = 70

4x = 76

x = 19

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.