Explanation

Given:

• SI (Simple Interest) = 81

• P (Principal) = 450

• R (Rate) = 5%

• Time (T) = ?

Using the formula:

$$SI = frac{P times R times T}{100}$$

Substituting the values:

$$81 = frac{450 times 5 times T}{100}$$ $$81 = frac{2250 times T}{100}$$ $$81 = 22.5 times T$$ $$T = frac{81}{22.5}$$ $$T = 3.6 text{years}$$

Explanation

To have infinite solutions, the two equations must be proportional, meaning:

(3x + 2y = 7)  

(6x + my = 14)

Compare coefficients:

- 6x / 3x = 2  

- 14 / 7 = 2  

→ So, m/2 must also be 2 → m = 4

Explanation

 Let present age = x

Given:

x + 15 = 4x − 15

→ 15 + 15 = 4x − x

→ 30 = 3x

→ x = 10

Explanation

Explanation

 In a 5-class arrangement where the number of rows and columns are equal, this means:

Rows=Columns

If the number of rows is given as K, then the number of columns will also be K.

Explanation

${x^}^2+18x+81=0$:

• The first term is x^2, so $a=x$.
• The last term is 81, so ${b^}^2=81$, which means $b=9$ (we take the positive root since the middle term is positive).
• The middle term is 18x. Let's check if it matches 2ab: $2(x)(9)=18x$. It does.

Therefore, the quadratic expression ${x^}^2+18x+81$ can be factored into $(x+9{)^}^2$.

So the factor form of the equation ${x^}^2+18x+81=0$ is $(x+9{)^}^2=0$.

Explanation

Given:

Time taken by A and B to complete the work = 12 days

Time taken by B and C to complete the work = 8 days

Time taken by C and A to complete the work = 6  days

Formulae used:

Time = Total work / Efficiency

Calculation:

Let us assume the total work is 1 unit.

⇒ A and B complete 1 unit work in 12 days → (A and B)'s 1 day's work = 1/12​

⇒ B and C complete 1 unit work in 8 days → (B and C)'s 1 day's work = 1/8​

⇒ A and C complete 1 unit work in 6 days → (A and C)'s 1 day's work = 1/6​

Adding everyone's 1 day's work:

$\Rightarrow 2(A+B+C)=(1/12+(1/8)+(1/6)$

⇒A+B+C=9/48​

= A, B, and C's 1 day's work = 9/48

⇒ B's 1 day's work = $(A+B+C)-(A+C)$

⇒ B's 1 day's work =(9/48)−(1/6) = 9-8 x/48 = 1/ 48 ​

​

⇒ B completes 1/48​ of the work in 1 day.

Therefore, B alone will take 48 days to complete the work.

Explanation

Percentage present = (Present / Total) × 100  

= (170 / 200) × 100  

= 85%

Explanation

Let the circumference of the circle = perimeter of the square = P  

- Circumference of circle = 2πr  

- Perimeter of square = 4a (a = side of square)  

So, 2πr = 4a ⇒ a = (πr)/2

- Area of circle = πr²  

- Area of square = a² = (πr/2)² = (π²r²)/4

Now compare:

πr² (circle) vs. (π²r²)/4 (square)  

Divide both sides:  

(πr²) / ((π²r²)/4) = 4/π > 1 ⇒ area of circle > area of square.

Explanation

These are two horizontal lines:

y = 2 and y = -5 are parallel and never intersect