Explanation

Profit = 5000 - 4000 = Rs. 1000

Profit % = (1000 / 4000) × 100 = 25%

Explanation

Explanation

The complement of a null set (∅) includes all elements of the universal set (U).

Since ∅ contains nothing, its complement is everything in U, so ∅' = U.

Explanation

Given:

Breadth = 1/5 × Length

Perimeter = 24m

Let length = L

Breadth = L/5

Perimeter formula: P = 2(L + B)

24 = 2(L + L/5)

24 = 2(6L/5)

24 = 12L/5

24 × 5 = 12L

120 = 12L

L = 10m

Explanation

Let's solve this problem:

Initially, food is enough for 36 people for 20 days.

Total food = 36 people * 20 days = 720 people-days

When 12 more people come, the total number of people becomes:

36 + 12 = 48

Now, let's find out how many days the food will last for 48 people:

720 people-days / 48 people = 15 days

Explanation

Given Ahmed's income is Rs. 85,000 and expenditure is Rs. 51,000:

The ratio of income to expenditure is 85,000 : 51,000.

To simplify, divide both parts by their greatest common divisor, which is 17,000:

85,000 / 17,000 = 5

51,000 / 17,000 = 3

So, the ratio is 5:3.

Explanation

Given:

Arc length = 2.5 cm

Diameter = 6 cm, so radius (r) = 3 cm

The formula for arc length is:

Arc length = θr

2.5 = θ * 3

θ = 2.5 / 3

θ = 0.833

Explanation

Coterminal angles differ by full rotations of 360°.

To find a coterminal angle of -60°, add or subtract 360°:

-60° + (-360°) = -420° → This is coterminal with -60°.

So, -420° and -60° share the same terminal side.

Explanation

A compass is used for drawing circles and arcs.

It has a pointed end for the center and a pencil or pen for marking the circle.

Explanation

To find the value of a² + b²:

Use the identity:

a² + b² = (a - b)² + 2ab

Given a - b = 3 and ab = 5:

a² + b² = (3)² + 2(5)

= 9 + 10

= 19