0.0135 of 270 + 0.07 of 441

= 3.645 + 30.87

= 34.51

Solve the given question, using following laws of indices,

Laws of Indices,

1-: a^m × aⁿ = a^{{m + n}}

2-: a^m ÷ aⁿ = a^{{m - n}}

3-: [(a^m)ⁿ] = a^mn

Solve the given question, using following laws of indices,

Laws of Indices,

1-: a^m × aⁿ = a^{{m + n}}

2-: a^m ÷ aⁿ = a^{{m - n}}

3-: [(a^m)ⁿ] = a^mn

Let, the number is = x

According to problem,

⇒ (3675/x²) × 37 = 2775

⇒ 3675/x² = 2775/37

⇒ 3675/x² = 75

⇒ x² = 49

⇒ x = 7

Concentration of Alcohol in the first bottle = 40%

Concentration of Alcohol in the second bottle = 19%

We know that,

For first bottle,

26 - 19 = 7

For second bottle,

40 - 26 = 14

Hence the ratio is 1 ∶ 2.

The part of Brandy replaced = 2/3

∴ The part of Brandy replaced is 2/3

From the given data,

⇒ x² – 15x + 56 = 0

⇒ x² - 7x - 8x + 56 = 0

⇒ x (x - 7) - 8 (x - 7) = 0

⇒ (x - 7)(x - 8) = 0

∴ x = 7 and x = 8

Also given that y² – 4y - 5 = 0

⇒ y² + y - 5y - 5 = 0

⇒ y (y + 1) - 5 (y + 1) = 0

⇒ (y - 5)(y + 1) = 0

∴ y = 5 and y = - 1

When x = 7 and y = 5, then x > y

When x = 7 and y = - 1, then x > y

When x = 8 and y = 5, then x > y

 x = 8 and y = - 1, then x > y

∴ x > y

From the given data,

⇒ x² + 6x + 9 = 0

⇒ x² + 3x + 3x + 9 = 0

⇒ x (x + 3) + 3 (x + 3) = 0

⇒ (x + 3)(x + 3) = 0

∴ x = - 3

Also from the given data,

⇒ y² + 4y + 4 = 0

⇒ y² + 2y + 2y + 4 = 0

⇒ y (y + 2) + 2 (y + 2) = 0

⇒ (y + 2)(y + 2) = 0

∴ y = - 2

When x = - 3 and y = - 2, then x < y

Speed of train A, S_A = 36 km/h = 36 × (1000/3600) m/s = 10 m/s

Speed of train A, S_B = 54 km/h = 54 × (1000/3600) m/s = 15 m/s

Length of train A, L_a = 250 m

Time taken for train B to overtake train A = 2 min = 120 s

Let the length of train B be L_b.

Time taken to overtake train A by train B = (L_a + L_b)/(S_B – S_A)

⇒ (250 + L_b)/(15 – 10) = 120

⇒ 250 + L_b = 600

⇒ L_b = 350 m

∴ length of train B is 350 m.

We know the formula for calculating Simple Interest.

SI = (P × r × t)/100

Where,

SI = Simple Interest

P = Principal

r = Rate of interest (in percentage)

t = Time period

From the given data,

Total amount lent = Rs. 12000

Rate of interest for Ram = 7%

Rate of interest for Shyam = 3%

t = 5 years

Total Simple interest received = Rs. 2000

Let the amount lent to Ram be Rs. x.

⇒ Amount lent to Shyam = Rs. (12000 - x)

So,

[(x × 7 × 5)/100] + [{(12000 - x) × 3 × 5}/100] = 2000

⇒ 35x + 180000 - 15x = 200000

⇒ 20x = 20000

⇒ x = Rs. 1000

∴ The amount lent to Ram = Rs. 1000

We know that, volume of a cube = a³

Volume of cubes of 3 cm, 4 cm and 5 cm sides = 3³ + 4³ + 5³ cm³

= 27 + 64 + 125 = 216 cm³

Surface area of the smaller cubes = 6(9 + 16 + 25) = 6 × 50 = 300 cm²

Since the large cube is obtained by melting the three smaller cubes,

Thus, volume of larger cube = sum of volumes of three smaller cubes = 216 cm³

Side of larger cube aa = ∛216 cm = 6 cm

Surface area of larger cube = 6 × a² cm², where a = length of each side of a cube

= 6 × 6² = 216 cm²