The correct answer is option 3 i.e. 37 minutes 30 seconds

Let the speed of A, B, and C be 5x, 4x, and 6x respectively.

Time difference = 1500/5x - 1500/6x

⇒ 5 = 1500(1/5x - 1/6x)

⇒ 1/300 = (6 - 5)/30x

⇒ x = 10

Speed of B = 4(10) = 40 m/min

Time taken by B = 1500/40

⇒ 37.5 minutes or 37 minutes 30 seconds

The correct answer is option 2 i.e. 50 years.

The present of the boy = 2/5 of his father's age

The present age of his mother = 34 years

Before 6 years, the age of the boy = 1/2 of his mother's age.

The present age of his mother = 34 years

Before 6 years, the age of his mother = 34 - 6 = 28 years.

Before 6 years Boy's age = 1/2 of his mother's age

= 1/2 × 28 = 14 years

The present age of the boy = 14 + 6 = 20 years

The present age of the boy = 2/5 of his father's age

20 = 2/5 × His father's age

His father's age = 20 × 5/2 = 50 years

The correct answer is Option 1 i.e. 36.

Let the average temperature for the first week and the following weeks be x₁, x₂, x_3, and x₄. Therefore, we get

Now, from this, we can get:

⇒ (x₂ + x₃ + x₄ ) - ( x₁ + x₂ + x₃ ) = 117 - 105

⇒ x₄ - x₁ = 12

The correct answer is option 3 i.e. 3500.

Given:

The ratio of father to son and son to daughter is 5 : 2

The daughter gets Rs. 400.

Calculations:

The ratio of share of father to son and son to daughter

Father : Son = 5 : 2 ------ (1)

Son : Daughter = 5 : 2 ------ (2)

Multiply equation (1) with 5 and equation (2) with 2 to balance the share of son

Father : Son = 25 : 10

Son : Daughter = 10 : 4

Father : Son : Daughter = 25 : 10 : 4

Let the share be 25x, 10x and 4x

If the value of 4x = 400

⇒ x = 100

Sum of share of father and son = 25x + 10x

Put the value of x

= 35x

= 35 × 100

= 3500

The correct answer is option 2 i.e. 3 years.

Principal = Rs. 64000

Rate = 25% per annum

CI = Rs. 61000

So,

Amount = 64000 + 61000 = Rs. 125000

Applying the formula for CI:

125000 = 64000 × (1 + 25/100)^T

⇒ (1 + 25/100)^T = 125/64

⇒ (5/4)^T = 125/64

⇒ (5/4)^T = (5/4)³

So,

T = 3

Hence,

Time for which the sum is invested = 3 years

The correct answer is Option 1 i.e. A > B.

A = 25% more than 36

⇒ A = 36 × (100 + 25)/100 = 45

⇒ B = 36% more than 25

⇒ B = (100 + 36)/100 × 25 = 34

∴ A > B

The correct answer is option 4 i.e. 525 : 128

The ratio of salary of Varun to his income other than salary = 42000: 10240

=  525 : 128.

The correct answer is option 3 i.e. 840.

Given sides - 15cm, 112cm, and 113 cm (forms a triplet)

Hence,

Area of triangle = (1/2) × B × H

⇒ (1/2) × 112 × 15

⇒ 56 × 15 = 840 cm²

The correct answer is option 1 i.e. 384π cm³.

The height and base radius of the cylinder are 3x and 4x, respectively.

Total surface area of the cylinder = 2πr(h + r)

704 = 2 × (22/7) × 4x × (3x + 4x)

⇒ 704 = 176x/7 × (3x + 4x)

⇒ 704 = 176x²

⇒ x² = 4

⇒ x = 2

Base radius = 4x = 8 cm

Height = 3x = 6 cm

Volume of the cylinder = πr²h = π × 64 × 6 = 384π cm³

The correct answer is option 2 i.e. -1/2.

Cos(90 + Ø) = -SinØ

Cos(180 + Ø) = -CosØ

Cos(360 - Ø) = CosØ

Given,

Cos180° + Cos135°- Cos240°+ Cos315°

⇒ Cos(90 + 90) = -Sin90 = -1

⇒ Cos(90 + 45) = -Sin45 = -1/√2

⇒ Cos(180 + 60) = - Cos60 = -1/2

⇒ Cos(360 - 45) = Cos45 = 1/√2

Now,

Cos180° + Cos135°- Cos240°+ Cos315° =  -1 - 1/√2 + 1/2 + 1/√2 = -1/2