Explanation

To find the greatest number that divides 36, 44, and 52 completely, we need to find their Highest Common Factor (HCF).

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Factors of 44: 1, 2, 4, 11, 22, 44

Factors of 52: 1, 2, 4, 13, 26, 52

The greatest common factor is 4.

Explanation

Let Haider's son's present age be x.

Haider's present age = 3x

After 10 years:

Son's age = x + 10

Haider's age = 3x + 10

The sum of their ages after 10 years will be 76:

x + 10 + 3x + 10 = 76

4x + 20 = 76

4x = 56

x = 14

Haider's present age = 3x = 3 × 14 = 42

Explanation

Let's factorize 2x^2 - 7x + 3. We need to find two numbers that multiply to 2 × 3 = 6 and add to -7. These numbers are -6 and -1.

So, 2x^2 - 7x + 3 = 2x^2 - 6x - x + 3

= 2x(x - 3) - 1(x - 3)

= (2x - 1)(x - 3)

Explanation

To add 2/9 and 1/3, we need a common denominator, which is 9.

1/3 = 3/9

Now, add:

2/9 + 3/9 = 5/9

Explanation

The cost of 3 books is Rs. 126. To find the cost of 8 books, we need to find the cost of 1 book first.

Cost of 1 book = 126 / 3 = 42

Cost of 8 books = 42 × 8 = 336

Explanation

To round off 87.321756 to 5 significant figures, we look at the 6th significant figure, which is 6.

Since it's greater than 5, we round up the 5th significant figure.

87.321756 becomes 87.322

Explanation

To find out how many persons are required to arrange 725 books in 5 hours, let's first determine the rate at which the persons arrange books.

11 persons arranged 319 books in 4 hours.

Rate = 319 books / (11 persons * 4 hours) = 319 / 44 = 7.25 books per person per hour.

Now, let's calculate how many persons are needed to arrange 725 books in 5 hours at the same rate:

Total work = 725 books

Time = 5 hours

Rate per person = 7.25 books per hour

Persons required = Total work / (Rate per person * Time)

= 725 / (7.25 * 5)

= 725 / 36.25

= 20

Explanation

To find the cost price (CP) of the can of oil, we can use the formula:

CP = (Selling Price × 100) / (100 - Loss Percentage)

Given Selling Price (SP) = Rs. 7786 and Loss Percentage = 15%,

CP = (7786 × 100) / (100 - 15)

= (7786 × 100) / 85

= 7786 × 20 / 17

= 9160

Explanation

Let's denote the number as x. The problem states that the difference between 72 and 7 times a number is 16.

We can set up the equation:

72 - 7x = 16

Subtract 72 from both sides:

-7x = 16 - 72

-7x = -56

Divide both sides by -7:

x = -56 / -7

x = 8

Explanation

The mode is the value that appears most frequently in the data set.

In the given data set (3, 5, 7, 8, 9), each value appears only once.

Since no value appears more than once, there is no mode.