Explanation

Explanation

Discount = 15% of 80

= 0.15 * 80

= 12

Sale price = Original price - Discount

= 80 - 12

= 68

Explanation

Given that x added to itself 13 times gives 112:

x + 13x = 112

14x = 112

x = 112 / 14

x = 8

Explanation

Explanation

Explanation

Work done by 12 children in 16 days = 1 (full work)

Work done by 1 child in 16 days = 1/12

Work done by 1 child in 1 day = 1/(12 × 16) = 1/192

Work done by 8 adults in 12 days = 1

Work done by 1 adult in 12 days = 1/8

Work done by 1 adult in 1 day = 1/(8 × 12) = 1/96

Work done by 16 adults in 3 days = 16 × 3 × (1/96) = 1/2

Remaining work = 1 - 1/2 = 1/2

Now, 6 adults and 4 children work together:

Work done by 6 adults in 1 day = 6 × 1/96 = 6/96 = 1/16

Work done by 4 children in 1 day = 4 × 1/192 = 4/192 = 1/48

Total work done per day = (1/16 + 1/48) = (3 + 1)/48 = 4/48 = 1/12

Days required = (1/2) ÷ (1/12) = 6 days

Explanation

The average of the first n natural numbers is given by (n + 1) / 2.

For n = 97:

Average = (97 + 1) / 2

= 98 / 2

= 49

Explanation

Given numbers: 8, 13, 25, 43, 11

Step 1: Add the numbers  

8 + 13 + 25 + 43 + 11 = 100

Step 2: Divide by the number of values  

100 ÷ 5 = 20

Explanation

20 men can construct a building in 40 days.

Total work = 20 men × 40 days = 800 man-days.

Time = Total work / Number of men = 800 man-days / 10 men = 80 days.

Explanation

We are told:

• Circumference of a circle = a

• Area of the circle = b

• And a = b

We know the formulas:

• Circumference:

  $$a = 2pi r$$
  

• Area:

  $$b=\pi r^2$$r=0orr=

Since $a = b$, set the formulas equal:

$$2pi r = pi r^2$$

Divide both sides by $pi$:

$$2r = r^2$$

Rearrange:

$$r^2 - 2r = 0 Rightarrow r(r - 2) = 0$$

So the solutions are:

r=0 or r=2