Explanation

 We are given the equation:

30y=60

To find the value of y, divide both sides by 30:

𝑦=60/30=2

Explanation

To find the percentage of profit, use the formula:

$$text{Profit$$Cost PriceSelling )×100

Given:
Cost Price (CP) = Rs. 500
Selling Price (SP) = Rs. 800

$$text{Profit} = 800 - 500 = 300$$ $$text{Profit$$500​)×100=60%

Explanation

√3, √4, √5 →  3+4=7 =5 Not valid

Explanation

Find HCF of 408, 468, and 516

• Prime factorizations:

  • 408 = $2^3\cdot 3<br>$

  • 468 = $2^2 cdot 3 cdot 13$
    

  • 516 = $2^2\cdot 3\cdot 43$

Common: 2^2.3 = 4.3=12

Explanation

Let angle = $x$
Complement = $90 - x$, Supplement = $180 - x$
Given:

$$6(90 - x) = 2(180 - x) - 12 \ 540 - 6x = 360 - 2x - 12 \ 540 - 6x = 348 - 2x \ 192 = 4x Rightarrow x = 48$$

$$540-6x=360-2x-12$$

$$540-6x=348-2x$$

$$192=4x\Rightarrow x=48$$

Explanation

To find LCM of fractions:

$$text{LCM} = frac{text{LCM of numerators}}{text{HCF of denominators}}$$HCF of denominators​

Numerators: 2, 3, 6 → LCM = 6
Denominators: 5, 10, 25 → HCF = 5

$$$$

text{LCM} = frac{6}{5}

Explanation

Step-by-step:

$$frac{31 times 3}{100} = frac{93}{100}, quad frac{7}{5} = frac{140}{100}, quad 20 = frac{2000}{100}$$

Add all:

93+140+2000​/100=2233​/100=22.33

Explanation

Multiply both sides by 2:

$$|3x| = 6 Rightarrow 3x = ±6 Rightarrow x = ±2$$

Explanation

Explanation

If4^a=8^b, find the ratio $frac{a}{b}$

Write both sides with base 2:

$$4^a = (2^2)^a = 2^{2a} \ 8^b = (2^3)^b = 2^{3b} Rightarrow 2^{2a} = 2^{3b} Rightarrow 2a = 3b Rightarrow frac{a}{b} = frac{3}{2}$$

⇒2^2a=2^3b⇒2a=3b⇒a​/b=3/2​