The correct answer is option 3 i.e. (1) is greater by 0.34%.

(1) Let the cost price of the article be 100 units.

After applying a discount of 12%

⇒ 100 × (100 - 12)/100 = 88

After applying a discount of 18%

⇒ 88 × (100 - 18)/100 = 72.16

Total discount: 100 - 72.16 = 27.84%

(2) A discount of 27.5%

(1) is greater than (2) by 0.34%

The correct answer is option 4 i.e. 4.5.

Total quantity to be filled in the tank = LCM(3, 5) = 15 units

⇒ Efficiency of new pipe = 15/3 = 5 units

⇒ Efficiency of the hole = 15/5 = -3 units

Total work in 1 hour = 5 - 3 = 2 units

Total number of hours = 15/2 = 7.5 hours

Number of hours when there is no hole = 3 hours

⇒ 7.5 - 3 = 4.5 hours

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

Let the length of the side of the equilateral triangle be x cm

∴ Height of prism = √3x

Volume of prism = √3/4 × side² × Height

⇒ 48 = √3/4 × x² × (√3)x

⇒ 64 = x³

⇒ x = 4 cm

The correct answer is option 3 i.e. 80°.

O is the orthocentre of ΔABC

And

∠BOC = 100°

In the figure:

∠OPA = ∠OQA = 90°

And

∠BOC = ∠POQ = 100°

In quadrilateral APOQ:

∠APO + ∠POQ + ∠OQA + ∠ QAP = 360°

⇒ 90° + 100° + 90° + ∠QAP = 360°

⇒ ∠QAP = 360° – 280° = 80°

The correct answer is option 4 i.e. 54.

⇒ 6³ × 15⁴ × 18²

⇒ 2³ × 3³ × 3⁴ × 5⁴ × 2² × 3⁴

⇒ 2⁵ × 3¹¹ × 5⁴

All perfect squares have odd factors.

⇒ (2²)² × (3²)⁵ × (5²)²

The number of factors of the given number as we have converted the real number into the nearest square.

⇒ Number of factors = (2 + 1)(5 + 1)(2 + 1)

⇒ 3 × 6 × 3

⇒ 54

The correct answer is Option 3 i.e. 1.69% loss.

Cost Price = Selling Price × 100/(100 + profit %)

Cost Price = Selling Price × 100/(100 - loss %)

The cost price of the first article(gain is 13%) = (100 × 9831)/113 = 8700

The cost price of the second article(loss is 13%) = (100 × 9831)/87 = 11300

So,

Total cost price of both the articles = 8700 + 11300 = 20000

Total selling price = 9831 × 2 = 19662

⇒ Loss = 20000 - 19662 = 338

Loss% =  (Loss)/Cost price × 100

⇒ % loss = (338/20000) × 100 = 1.69

The correct answer is option 3 i.e. 10.

Given:

3^{x + 2} - 3^x = 72

Concept used:

A^{m + n} = A^m.Aⁿ ------ (1)

A^x = A^y then x = y because the base of the number is the same. ------ (2)

Calculations:

Using concept (1) in the given equation

⇒ 3^x.3² -  3^x = 72

⇒ 3^x (9 - 1) = 72

⇒ 3^x × 8 = 72

⇒ 3^x = 72/8

⇒ 3^x = 9

⇒ 3^x = 3²

Using concept (2), we get

⇒ x = 2

⇒ x² + 2x + 2. ----- (3)

Put the value of x in equation (3)

⇒ 4 + 4 + 2 = 10

The correct answer is Option 3 i.e. 41 km.

Concept:- If a person covers a distance in t hours, with the speed of p km/hr in the first half and with the speed of q km/hr in the second half, then the total distance D covered by him is

D = 2 × t × (p × q)/(p + q)

Now, according to the question

Distance covered by Arpit

D₁ = 2 × 3.5 × (12 × 15)/(12 + 15)

⇒ D₁ = 1260/27

⇒ D₁ = 46.66 or 47 km

Distance covered by Arpita

D₂ = 2 × 4 × (18 × 20)/(18 + 20)

⇒ D₂ = 2880/38

⇒ D₂ = 75.78 or 76 km

Total distance = D₁ + D₂ = 47 + 76 = 123

one third of 123 = 1/3 × 123 = 41 km

The correct answer is option 3 i.e. 5/8 > 25/49 > 78/155 > 12/25.

Simplifying the given fractions,

We could observe that,

5/8 = 0.625

25/49 = 0.510

78/155 = 0.503

12/25 = 0.48

So, the correct descending order = 5/8 > 25/49 > 78/155 > 12/25