Read the following text and answer the following questions on the bas...
Number of workers = x
Number of workers when increased by 2 = x + 2
∴ Number of boxes prepared by the workers
(x + 2) = (x + 3) [2 + 3 (x + 2)
= 7 [2 + 3 × 7] [∵ x = 5]
= 7 × 23
= 161.
View all questions of this test
Read the following text and answer the following questions on the bas...
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 working in the industry.
- The number of boxes produced in a particular day was 85.
To find:
- How many boxes will be prepared when the number of workers is increased by 2.
Solution:
Let's assume the number of workers in the industry is 'x'.
According to the given information, the number of boxes prepared by each worker is 2 more than thrice the number of workers. So, we can write the equation as:
Number of boxes prepared by each worker = 3x + 2
Since each worker produces a certain number of boxes, to find the total number of boxes produced in a day, we need to multiply the number of boxes prepared by each worker by the total number of workers. So, the equation becomes:
Total number of boxes produced in a day = (3x + 2) * x
It is given that the number of boxes produced in a particular day was 85. So, we have:
(3x + 2) * x = 85
Simplifying the equation:
3x^2 + 2x = 85
3x^2 + 2x - 85 = 0
To solve this quadratic equation, we can factorize it or use the quadratic formula. In this case, let's use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
For the given equation, a = 3, b = 2, and c = -85. Substituting these values into the quadratic formula:
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
Taking the positive value:
x = (32 - 2) / 6
x = 30 / 6
x = 5
So, the number of workers in the industry is 5.
Now, let's find the number of boxes that will be prepared when the number of workers is increased by 2.
New number of workers = 5 + 2 = 7
Number of boxes prepared by each worker = 3x + 2
Number of boxes prepared by each worker = 3 * 7 + 2
Number of boxes prepared by each worker = 21 + 2
Number of boxes prepared by each worker = 23
Total number of boxes produced in a day = Number of boxes prepared by each worker * Total number of workers
Total number of boxes produced in a day = 23 * 7
Total number of boxes produced in a day = 161
Therefore, when the number of workers is increased by 2, a total of 161 boxes will be prepared. Hence, the correct answer is option 'A'.
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.