Explanation

The arithmetic mean (average) of 25 values is 10, so we can set up the equation:

Sum of values / 25 = 10

Multiply both sides by 25:

Sum of values = 25 × 10

Sum of values = 250

So, the correct answer is: 250

Explanation

We can set up the proportion as:

6/m = 9/12

Cross-multiply:

6 × 12 = 9 × m

Simplify:

72 = 9m

Divide both sides by 9:

m = 72/9

m = 8

So, the correct answer is: 8

Explanation

12x + 17 = 65

Subtract 17 from both sides:

12x = 65 - 17

12x = 48

Divide both sides by 12:

x = 48/12

x = 4

Explanation

Since the area of the rectangle is 50 cm² and the length is 10 cm, we can use the formula:

Area = Length × Width

Substitute the values:

50 = 10 × Width

Divide both sides by 10:

Width = 50/10

Width = 5

So, the width is 5 cm.

Explanation

Since the ratio of cats to dogs is 2:3, we can write:

Number of cats / Number of dogs = 2/3

We know there are 18 dogs, so:

Number of cats / 18 = 2/3

Cross-multiply:

Number of cats = (2/3) × 18

Simplify:

Number of cats = 2 × 6

Number of cats = 12

So, there are 12 cats.

Explanation

Since the shop sells the pair of shoes for Rs. 800 after a 20% discount, that means the discount amount is 20% of the original price.

Discount amount = 20% of x = 0.20x

The selling price (Rs. 800) is the original price minus the discount amount:

800 = x - 0.20x

Simplify the equation:

800 = 0.80x

Divide both sides by 0.80:

x = 800 / 0.80

x = 1000

So, the original price for the pair of shoes was:

Rs. 1000

The correct answer is: Rs. 1000

Explanation

To solve for x, we need to isolate x on one side of the equation.

3x + 2 = 11

Subtract 2 from both sides:

3x = 11 - 2

3x = 9

Divide both sides by 3:

x = 9/3

x = 3

So, the correct answer is: 3