Explanation

We are given an arithmetic progression (AP):

10, 7, 4, ...

Step 1: Identify the first term and common difference

First term a = 10

Common difference d = 7 - 10 = -3

Step 2: Use the formula for the nth term of an AP:

Tₙ = a + (n - 1) × d

Find the 30th term (T₃₀):

T₃₀ = 10 + (30 - 1) × (-3)

T₃₀ = 10 + 29 × (-3)

T₃₀ = 10 - 87 = -77

Explanation

30% of x = 21 → (30/100) × x = 21 → x = 21 × (100/30) = 70

Now find what percent 49 is of 70: (49 / 70) × 100 = 70%

Explanation

Calculate stepwise:

120% of 6250 = (120/100) × 6250 = 7500

12% of 7500 = (12/100) × 7500 = 900

20% of 900 = (20/100) × 900 = 180

Explanation

Combine terms: (2x/24) + (x/24) = 0 → (3x/24) = 0

Multiply both sides by 24: 3x = 0 → x = 0

Explanation

Prime number: A prime number is a number that can be divided only by one and the number itself.

Example - 2, 3, 5, ..etc.

Formula used:

The arithmetic mean = Sum of all terms/ Number of terms

Calculation:

According to the question,

First 10 prime numbers = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

The arithmetic mean = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29)/10

⇒ 129/10 = 12.9

The arithmetic mean of the first ten prime numbers is 12.9.

Explanation

Given: a/b = 3/5 ... (1)

When 2 is added to both numbers, the ratio becomes 2/3, so we can write:

(a+2)/(b+2) = 2/3 ... (2)

Cross-multiplying (2), we get:

3(a+2) = 2(b+2)

Expanding and simplifying, we get:

3a + 6 = 2b + 4

Subtracting 6 from both sides gives:

3a = 2b - 2

Now, substituting (1) in the above equation, we get:

3(3/5)b = 2b - 2

Multiplying both sides by 5, we get:

9b = 10b - 10

Subtracting 10b from both sides gives:

-b = -10

Dividing both sides by -1, we get:

b = 10

So, the correct answer is: 10

Explanation

Let's break down the problem step by step:

Step 1: Express the initial number of boys and girls using the given ratio

Let the number of boys be 11x and the number of girls be 13x.

Step 2: Calculate the new number of boys and girls after 4 boys and 8 girls join the class

New number of boys = 11x + 4

New number of girls = 13x + 8

Step 3: Set up the equation based on the new ratio

Given the new ratio is 4:5, we can write the equation as:

(11x + 4) / (13x + 8) = 4/5

Step 4: Solve the equation

Cross-multiplying gives us:

5(11x + 4) = 4(13x + 8)

55x + 20 = 52x + 32

55x - 52x = 32 - 20

3x = 12

x = 4

Step 5: Calculate the strength of the class

Strength of the class = Initial number of boys + Initial number of girls + New boys + New girls

= 11x + 13x + 4 + 8

= 24x + 12

= 24*4 + 12

= 96 + 12

= 108

Explanation

The pattern decreases by 5, then 5 again:

18 → 13 (minus 5)

13 → 8 (minus 5)

8 → 3 (minus 5)

Explanation

Step 1: Let the marked price be Rs. x.

Since items are sold at 10% less than the marked price,
The selling price (SP) = $x-10\%\text{ of }x=0.9x$

Step 2: Desired profit = 10% on cost

Cost price (CP) = Rs 90
Profit = 10% of 90 = Rs 9
So, desired Selling Price (SP) =Rs 90 + Rs9 = Rs 99

Step 3: Set up the equation

We already said that the selling price is 0.9x, so:

$$0.9x = 99$$

Step 4: Solve for x

$$x = frac{99}{0.9} = 110$$

Explanation

Step 1: Understand the meaning

We are given two ratios and asked to find a common multiple — that is, a set of values for M, N, and O that fits both ratios proportionally.

Given Ratios:

1. M : N : O = 2 : 3 : 5

2. M : N : O = 4 : 5 : 6

We want to find a new ratio X : Y : Z that is proportional to both these given ratios.

Step 2: Check Option B: 8:15:30

Try simplifying 8:15:30:

Divide all terms by 1 (GCD is 1, so already simplified):
Still 8:15:30

Now check if it fits the first ratio (2:3:5):

• 8 ÷ 2 = 4

• 15 ÷ 3 = 5

• 30 ÷ 5 = 6

So 8:15:30 = 2×4: 3×5: 5×6 = 2:3:5 scaled up by different amounts?
No — wait! Those aren’t consistent scalings.

Instead, let’s try another way:

Divide 8:15:30 by 4:

• 8 ÷ 4 = 2

• 15 ÷ 5 = 3

• 30 ÷ 6 = 5

So 8:15:30 → 2:3:5  (matches first ratio)

Now divide 8:15:30 by 2:

• 8 ÷ 2 = 4

• 15 ÷ 3 = 5

• 30 ÷ 5 = 6

So 8:15:30 → 4:5:6  (matches second ratio)

8:15:30 is a common multiple of both 2:3:5 and 4:5:6