The correct answer is option 2 i.e. 21

(84 ÷ 12 × 3 − 4 ÷ 12 × 9 + 5 × 6 − 2 × 3)/(8 ÷ 12 × 3)

⇒ (7 × 3 - 3 + 30 - 6)/(2)

⇒ (21 - 3 + 30 - 6)/2

⇒ (51 - 9)/2

⇒ 42/2 = 21

The correct answer is option 2 i.e. 2312.

Smallest number divisible by 3, 5, 7, and 11 = LCM (3, 5, 7, 11)

⇒ 3 × 5 × 7 × 11 = 1155

Second smallest number = 2 × 1155 = 2310

To leave a remainder of 2, the number should be = 2310 + 2 = 2312

The correct answer is Option 1 i.e. 9.

4p75684q2 is divisible by 72, it will also be divisible by 8 and 9

Divisibility of 8 = Number formed by the last three digits must be divisible by 8

4q2 is divisible by 8, q must be 3 or 7

4p7568432 or 4p7568472 must be divisible by 9

Divisibility of 9 = sum of digits must be divisible by 9

4p7568432 = 4 + 7 + 5 + 6 + 8 + 4 + 3 + 2 + p = 39 + p; p must be 6

4p7568472 = 4 + 7 + 5 + 6 + 8 + 4 + 7 + 2 + p = 43 + p; p must be 2

p + q = 6 + 3 or 2 + 7 = 9

The correct answer is option 4 i.e. ₹8,166.67.

Amount A = ₹14,112

Rate = r = 20% per annum compounded annually

Time = n = 3 years

Principal = P = ?

A = P(1 + r/100)ⁿ

⇒ 14112 = P(1 + 20/100)³

⇒ 14112 = 216P/125

⇒ P = 49000/6 = Rs 8,166.67

The correct answer is option 3 i.e. Rs 24,000.

Given:

Total profit at the end of the year = Rs 50,000.

Explanation:

Let the total invested by P, Q and R be 100x.

Now, Investment of P = 20% of 100x = 20x

Remaining investment = 100x - 20x = 80x

Investment of Q = 40% of 80x = 32x

Investment of R = 100x - (20x + 32x) = 48x

So ratio of profits of P, Q and R = 20x : 32x : 48x = 5 : 8 : 12

Hence the investment of R is Rs 24,000.

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

Given that

The current population of the city is 10 lakhs

In the next 2 years, it will increase to 12.10 lakhs

Let the uniform annual rate of growth be r%

According to the question;

The Increased population after 2 years = The current population × (100 + r)/100 × (100 + r)/100

⇒ 12.10 = 10 × (100 + r)/100 × (100 + r)/100

⇒ (100 + r)² = 12100

⇒ 100 + r = 110

⇒ r = 110 - 100 = 10%

The correct answer is Option 4 i.e. Rs 60,000.

Let the total number of employees = 100

Number of workers = 65% of 100 = 65

Number of officers = 35% of 100 = 35

Let, the average monthly salary of officers and workers be x and y

Now,

⇒ x = Average monthly salary + 39000

⇒ x = (35x + 65y)/100 + 39000

⇒ 100x = 35x + 65y + 390000

⇒ 65x = 65y + 390000

⇒ 65x - 65y = 390000

⇒ 65(x - y) = 390000

⇒ x - y = 60000

Thus, the difference between the average salary of an officer and a worker is Rs.60000

The correct answer is Option 4 i.e. 70.

Efficiency of A : Efficiency of B = 3 : 1 and,

Time taken by B = 280 days

We know that,

Work = Efficiency × Time

Efficiency of B × Time of B = (Efficiency of A + B) × (Time taken by A and B together)

⇒ 1 × 280 = (3 + 1) × (Time taken by A and B together)

⇒ Time taken by A and B together = 280/4 = 70 days

The time taken by A and B together is 70 days.

The correct answer is option 2 i.e. 18.

Let, the length of rectangle be L meter.

The width of the rectangle (b) = (L - 2) meter

Perimeter of a rectangle = 2(l + b)

⇒ 2(l + b) = 68

⇒ L + L - 2 = 34

⇒ 2L = 36

⇒ L = 36/2 = 18 m

The correct answer is Option 4 i.e. 3 : 1.

The volume of cone = 1/3 𝜋r₁²h₁

here, r₁ = radius of cone, h₁ = height of cone

The volume of cylinder = 𝜋r₂²h₂

here, r₂ = radius of cylinder, h₂ = height of cylinder

Given that,

Volume of cone = volume of cylinder and,

⇒ r₁ = r₂

⇒ 1/3 𝜋r₁²h₁ = 𝜋r₂²h₂

⇒ h₁/h₂ = 3/1

⇒ h₁ : h₂ = 3 : 1