The correct answer is Option 4 i.e. 2 : 1.

Let Work done by 1 man in 1 hour be M units and that by 1 boy in 1 hour be B units

Work done by 1 man and 1 boy in 1 hour = (M + B)

Work done by 6 men and 3 boys in one hour = (6M + 3B)

According To Question -

⇒ (6M + 3B) = 5 × (M + B)

⇒ (6M + 3B) = (5M + 5B)

⇒ M = 2B

⇒ M : B = 2 : 1

The correct answer is option 1 i.e. 24.

[1664 ÷ 128 × 16] ÷ 13/4 = (8/3) × ?

Applying BODMAS Rule;

⇒ [13 × 16] ÷ 13/4 = (8/3) × ?

⇒ 16 × 4 = (8/3) × ?

⇒ (8/3) × ? = 64

⇒ ? = 24

The correct answer is option 3 i.e. 25%.

S.I = (P × R × T)/100

S.I = (13P - P) = 12P

⇒ 12P = (P × R × 48)/100 

⇒ 12 = (R × 48)/100

⇒ 1200 = (R × 48)

⇒ R = 25%

The correct answer is Option 1 i.e. 270 hours.

Let time taken by pipe A alone to fill the tank be x hours.

Tank filled by A alone in an hour = 1/x

Time taken by B alone to fill the tank = x/2 hours

Tank filled by B alone in an hour = 2/x

Time taken by C alone to fill the tank = (x/2)/3 = x/6 hours

Tank filled by C alone in an hour = 6/x

Together they can fill the tank in = 30 hours

The total amount of tank they can fill together in 1 hour = 1/30

According to the question-

⇒ 1/x + 2/x + 6/x = 1/30

⇒ 9/x = 1/30

⇒ x = 30(9) = 270 hours

The correct answer is Option 2 i.e. 180.

Required difference =  [(15% +23% + 15%) - (12% +17% + 18%)] of 3000

⇒ 6% of 3000

⇒ (6 × 30) = 180

The correct answer is option 4 i.e. 56.25%.

Let the cost of the bag be Rs 100.

Profit = 25%

So, the selling price = Cost price × (100 + profit%)/100

selling price = 100 × (100 + 25)/100 = 125

Let the marked price be Rs x.

So, the selling price would be 0.8x

According to the question,

⇒ 0.8x = 125

⇒ x = 156.25

Thus, the marked-up percentage = 156.25 - 100 = 56.25%

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

The correct answer is Option 1 i.e. 3.

Prime numbers are 2, 3, 5....

According to the question;

⇒ (27 × 2) = 54

Where 54 is not a perfect square

⇒ (27 × 3) = 81

81 is a perfect square of 9

Hence, the required number is 9

So, the smallest prime number will be 3

The correct answer is Option 2 i.e. 735.7 cm².

Side of the square = 24 cm

Perimeter of the square = 4 × side

Circumference of the circle = 2πr

According to the question;

⇒ 4 × 24 = 2πr

⇒ 4 × 24 = 2 × 22/7 × r

⇒ r = 15.3 cm

Now,

Area of the circle = πr² = 22/7 × 15.3²

⇒ 735.7 cm²