Read the following text and answer the following questions on the basis of the same:A small scale industry produces a certain boxes of candles in a day. Number of boxes prepared by each worked on a particular day was 2 more than thrice the number of workers working in the industry. The number of boxes produced in a particular day was 85.Q. Number of workers working in the industry:a)5b)6c)17d)8Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Let the workers are x, Number of boxes prepared by the workers

= 2 + 3x

According to the question,

x(2 + 3x) = 85

⇒ 3x² + 2x – 85 = 0

⇒ 3x² + 17x – 15x – 85 = 0

⇒ x(3x + 17) – 5(3x + 17) = 0 ⇒

⇒ (3x + 17)(x – 5) = 0

⇒ x = 5

Answer

How many
boxes will be prepared when the number of workers are increased by 2

Answer

Given:
- A small scale industry produces a certain number of boxes of candles in a day.
- The number of boxes prepared by each worker on a particular day was 2 more than thrice the number of workers.
- The total number of boxes produced in a particular day was 85.

To Find:
The number of workers working in the industry.

Solution:

Let's assume the number of workers in the industry as 'x'.

Number of boxes prepared by each worker:
According to the given information, the number of boxes prepared by each worker on a particular day was 2 more than thrice the number of workers. Mathematically, we can represent it as:
Number of boxes prepared by each worker = 3x + 2

Total number of boxes produced:
The total number of boxes produced in a particular day was given as 85.

So, we can set up the following equation:
Total number of boxes = Number of workers * Number of boxes prepared by each worker
85 = x * (3x + 2)

Solving the equation:
We need to solve the quadratic equation to find the value of 'x'.

85 = x * (3x + 2)
85 = 3x^2 + 2x
3x^2 + 2x - 85 = 0

To solve this quadratic equation, we can either factorize it or use the quadratic formula. Let's use the quadratic formula:

The quadratic formula is given by:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Here, a = 3, b = 2, and c = -85.

Substituting the values in the quadratic formula, we have:
x = (-2 ± sqrt(2^2 - 4(3)(-85))) / (2 * 3)
x = (-2 ± sqrt(4 + 1020)) / 6
x = (-2 ± sqrt(1024)) / 6
x = (-2 ± 32) / 6

Simplifying further, we have:
x = (30/6) or (-34/6)
x = 5 or -17/3

Since the number of workers cannot be negative or in fractions, we can conclude that the number of workers working in the industry is 5 (option A).

Therefore, the correct answer is option A.

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