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Let distance between Heath’s home and Lake is T km.

Total distance covered = T km + (20 km/hr × 1 hr) + T km = (2T + 20) km

Total time taken = (T/50 + 1 + T/50) hours = (T/25 + 1) hours = (0.04T + 1) hours

Average speed = Total distance covered/Total time taken

⇒ 38 = (2T + 20)/(0.04T + 1)

⇒ 1.52T + 38 = 2T + 20

⇒ T = 18/0.48 = 37.5

∴ Distance from home to lake is 37.5 km.

Given that:

Quantity of alloy = 150 kg

in this alloy copper and zinc ratio = 3 : 2

calculation:

If  overall alloy contain copper as 45%

(150 × 3/5 + 2X/5) = 45 % (150 + X)

⇒ (90 + 2X/5) = 9 (150 + X)/20

⇒ 1800 + 8X = 1350 + 9X

⇒ X = 450 kg

If overall alloy contain copper as 55%

(90 + 2X/5) = 55 (150 + X) / 100

⇒ 1800 + 8X = 1650 + 11X

⇒ x = 50 kg

∴  The minimum value of X is 50 kg.

Given:

Total amount to invest = Rs. 8425

Ages of daughters are 24 years and 28 years.

Formula used:

A = P(1 + r/100)ⁿ

Where, A = Amount

P = Principal

r = Rate

n= time

Calculation:

Let Principal of younger daughter be (P1) 

And, Let Principal of elder daughter be (P₂)

Time of elder daughter = (40 – 28) years = 12 years

Time of younger daughter = (40 – 24) years = 16 years

Rate = 33.3% = (100/3)%

According to the question:

Younger daughter = Elder daughter

P₁(1 + r/100)n = P₂(1 + r/100)n

⇒ P1[1 + (100/3 × 100)]¹⁶ = P2[1 + 100/3 ×100)]¹²

⇒ P1(4/3)16 = P2(4/3)12

⇒ P₁/P₂ = [(4/3)12/(4/3)16]

⇒ P1/P2 = [1/(4/3)⁴]

⇒ P1/P2 = (3/4)4

⇒ P1/P2 = 81/256

⇒ P1 : P2 = 81 : 256

Now, again let P₁ be 81x

Let P₂ be 256x

Total principal = (81x + 256x) = Rs. 337x

Again,

⇒ 337x = 8425

⇒ x = 8425/337 

P₂ = 256x = 256 × (8425/337) = Rs. 6400

∴ The share of elder daughter is Rs. 6400.

We know that,

Total surface area of a closed cylinder = area of curved surface + area of circular top and bottom

∴ Total surface area of closed cylinder = 2πrh + 2πr² = 2πr(r+h) sq. units

Where, r = radius of base of cylinder, h = height of cylinder

According to the condition given in the question,

Curved surface area = (3/4) ×Total surface area

$\therefore 2\pi rh; = \frac{3}{4} \times 2\pi r\left( {r + h} \right)$

⇒ 4h = 3 × (r + h)

⇒ h = 3r

Now, total surface area of a closed cylinder = 2πr(r + h) = 1232 cm²

∴ 2πr (r + 3r) = 1232

8πr² = 1232

$\Rightarrow {r^2} = \frac{{1232}}{{8\pi }} = ;49;c{m^2}$

⇒ r = 7 cm

∴ Volume of a right circular cylinder = πr²h cubic units

⇒ Volume of the given cylinder = π r² × 3r = 3π r³

⇒ Volume of the given cylinder = π r² × 3r = 3π r³ = 3234 cm³

Given:  

63.76 ÷ √(255.79) × {24.99% of (2.89)3} = (?)3

Concept Used:

Follow the BODMAS rule according to the table given below:

Calculation:

63.76 ÷ √(255.79) × {24.99% of (2.89)3} = (?)³

⇒ 64 ÷ √(256) × {25% of (3)3} = (?)³

⇒ 64 ÷ 16 × {(25/100) × 27} = (?)³

⇒ 4 × (27/4) = (?)³

⇒ 27 = (?)³

⇒ ? = 3

∴ 3 will come in place of the question mark ('?').

Given:

250 of 56 × 25% - 128% of 650 = ? × 6 + 1024

Concept Used:

Calculation:

250 of 56 × 25% - 128% of 650 = ? × 6 + 1024

⇒ 250 of 56 × 25% - 128 of 650% = ? × 6 + 1024

⇒ 250 × 56 × (25/100) - 128 × (65/10) = {(?) × 6} + 1024

⇒ 250 × 14 - 64 × 13 = {(?) × 6} + 1024

⇒ 3500 - 832 -1024 = (?) × 6

⇒ 1644 = (?) × 6

⇒ ? = 274

∴ The value of ? is 274.

Given:

19.99% of 249.99 + 34.99% of 299.97 - ? = 29.99% of 349.99

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

As we need to find out the approximate value, we can write these values to their nearest integers.

19.99% of 249.99 + 34.99% of 299.97 - ? = 29.99% of 349.99

⇒ 20% of 250 + 35% of 300 - ? = 30% of 350

⇒ (20/100) × 250 + (35/100) × 300 - ? = (30/100) × 350

⇒ 50 + 105 - ? = 105

⇒ ? = 50

∴ 50 should come in place of the question mark (?).

Correct answer is: 3

 

Concept used:

The BODMAS rule should be followed to solve the question as per the given table:

Calculation:

22% of 1250 + 1/7 of 1729 + 272 = ? - 132 - 24

⇒ 22/100 × 1250 + 1/7 × 1729 + 729 = ? - 169 - 24

⇒ 11 × 25 + 247 +729 = ? - 169 - 24

⇒ 275 + 247 + 729 = ? - 169 - 24

⇒ 1251 = ? - 169 - 24

⇒ ? = 1251 + 169 + 24

⇒ ? = 1444

 

∴The value of ? is 1444

Given:

37.5% of √576 + 150% of √1024 = (?) + 12.5% of 96

Concept Used:         

Calculation:

37.5% of √576 + 150% of √1024 = (?) + 12.5% of 96

⇒ 37.5% of 24 + 150% of 32 = (?) + 12.5% of 96

⇒ (3/8) of 24 + (3/2) of 32 = (?) + (1/8) of 96

⇒ 9 + 48 = (?) + 12

⇒ ? = 48 + 9 -12

⇒ ? = 45

∴ The value of ? is 45.

Let x be the number of books published by B in May

x + 100 be the number of books published by A in May

Now,

Number of books not distributed to the publisher by A in May

⇒ (30/100) × (x + 100)

Number of books not distributed to the publisher by B in May

⇒ (20/100) × x

According to the question

(50/100) × (30/100) × (x + 100) = (20/100) × x

⇒ 15 (x + 100) = 20x

⇒ 15x + 1500 = 20x

⇒ 5x = 1500

⇒ x = 300

∴ The number of books published by B in May is 300