The correct answer is Option 2 i.e. 7/9.

3x² + 3 + 5x = 0

Dividing by x, we get,

⇒ 3x + 3/x + 5 = 0

⇒ 3 (x + 1/x) = -5

⇒ (x + 1/x) = -5/3

Squaring both sides,

⇒ x² + 1/x² + 2 × x × 1/x = 25/9

⇒ x² + 1/x² = 25/9 - 2 = 7/9

The correct answer is Option 2 i.e. 1%.

Formula used:

Profit% = Profit/Cost Price × 100

Calculations:

Let the cost price of each laptop be Rs. 100

According to the question,

One laptop is sold at a 7% loss and the second laptop is sold at a 9% profit

The cost price of first laptop = Rs. 100

Loss% = 7%

Selling Price = Rs. 93

The cost price of second laptop = Rs. 100

Profit% = 9%

Selling Price = Rs. 109

Total cost price = 100 + 100 = Rs. 200

Total selling price = 93 + 109 = Rs. 202

Hence, Net profit = Rs. 202 - Rs. 200 = Rs. 2

Profit% = (2/200) × 100 = 1%

Short Trick:

As the cost price of both the laptops is same.

Hence, net profit/loss = (+9% + (-7%))/2 = + 1% profit

The correct answer is option 2 i.e. 5.

x = 5% of 4% of 2500

⇒ x = (1/20)(1/25)(2500)

⇒ x = 5

The correct answer is option 1 i.e. 1/104

HCF of fractions = HCF of numerators/LCM of the denominators

HCF of numerators = HCF of (5, 7, 15)

⇒ 1

LCM of the denominators = LCM of (13, 8, 2)

⇒ 104

HCF of fractions = 1/104

The correct answer is option 2 i.e. 30 days.

Suppose Sakshi takes K days to do the work.

∴ Sachi takes (2 × 3K/4) = (3/2)K days to it 

According to the question,

⇒ (Sakshi + Sachi)’s one day’s work = 1/18

Thus, 

⇒ (1/K) + (2/3K) = 1/18

⇒ K = 30

Hence, Sakshi takes 30 days.

The correct answer is option 2 i.e. Rs 540.

Assume the ratio in terms of x

Let the amount A gets = 3x and B gets = 5x and the total sum = 8x

A/Q, (3x - 22.5)/(5x + 22.5) = 1/2

2(3x - 22.5) = (5x + 22.5)

6x - 45 = 5x + 22.5

x = 67.5

So, the sum will be 8 × 67.5 = Rs. 540

The correct answer is Option 1 i.e. 37.27%.

Three successive discounts of 18%, 15%, and 10%

Successive discount = x + y - (xy)/100

⇒ 18 + 15 - (18 × 15)/100

⇒ 33 - 270/100

⇒ 33 - 2.7 = 30.3

Now, 

Again Successive discount

⇒ 30.3 + 10 - (30.3 × 10)/100

⇒ 40.3 - 3.03 = 37.27

So, the net discount is 37.27%.

The correct answer is Option 3 i.e. 5/72.

Here, given, 

The HCF of the two numbers is 12

So, let, the numbers are 12x and 12y (where x and y are co-prime numbers)

But also, the LCM of the numbers is 72

So, 12(xy) = 72

⇒ xy = 6

But, x and y are co-prime numbers so the values of (x,y) can be,

(1, 6), (2, 3), (3, 2) and (6, 1)

We can take any value of x and y from these

Let's take, x = 2 and y = 3

So, the numbers are, 24 and 36

Now,

⇒ 1/24 + 1/36 = 3/72 + 2/72 = 5/72

The correct answer is option 4 i.e. 1541.

Fourth proportional of a, b, and c = bc/a

⇒ Fourth proportional of 13, 23, 871 = (23 × 871)/13

⇒ (67 × 23) = 1541

The correct answer is option 1 i.e. -3.

The 6-digit number 479xy9 is divisible by each of 7, 11, 13

7 × 11 × 13 = 1001

If we multiply 479 to 1001, it gives us

479 × 1001 = 479479

So, x = 4

y = 7

So, x - y = 4 - 7 = -3