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

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 that log10 2, log10(2x - 1), and log10(2x + 3) are in AP:

2 * log10(2x - 1) = log10 2 + log10(2x + 3)

log10(2x - 1)^2 = log10(2 * (2x + 3))

(2x - 1)^2 = 2 * (2x + 3)

4x^2 - 4x + 1 = 4x + 6

4x^2 - 8x - 5 = 0

(2x + 1)(2x - 5) = 0

2x = 5 or 2x = -1 ( rejected since 2x > 0 for log(2x-1) and log(2x+3) to be defined)

2x = 5

x = log2 5

Explanation

Original price = Rs 800

Discount = 25% of 800

= 0.25 × 800

= Rs 200

Final price = Original price - Discount

= 800 - 200

= Rs 600

Explanation

Given equation:

x² - 5x + 6 = 0

Factor the quadratic equation:

(x - 2)(x - 3) = 0

This gives us:

x - 2 = 0 or x - 3 = 0

x = 2 or x = 3

The roots of the equation are x = 2 and x = 3.

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

To express 2.08 as a percentage:

2.08 × 100 = 208%

Explanation

The sequence of savings is:

4, 13, 22, ... with a common difference of 9.

Let's find the week when savings reach 130:

4 + (n-1)9 = 130

(n-1)9 = 126

n-1 = 14

n = 15

The savings will reach Rs 130 in the 15th week.

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

Let's denote A's rate of work as A, and B's rate of work as B.

Given A + B together complete the work in 12 days:

(A + B)'s 1 day's work = 1/12

B alone completes the work in 20 days:

B's 1 day's work = 1/20

A's 1 day's work = (A + B)'s 1 day's work - B's 1 day's work

= 1/12 - 1/20

= (5 - 3) / 60

= 2 / 60

= 1 / 30

A alone will complete the work in 30 days.