Ex.4.2 Q2 Quadratic Equations Solutions - NCERT Maths Class 10

Go back to  'Ex.4.2'

Question

Solve the problems given in example \(1.\)

(i) John and Jivanti had \(45\) marbles. Both of them lost \(5\) marbles each and the product of the no. of marbles they now have is \(124.\) We would like to find out how many marbles they had to start with?

(ii) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be \(55\) minus the number of toys produced in a day. On a particular day, the total cost of production was ₹\(750.\) We would like to find out the number of toys produced on that day.

 Video Solution
Quadratic Equations
Ex 4.2 | Question 2

Text Solution

(i)

What is known?

(i) John and Jivanti together had \(45\) marbles

(ii) Both of them lost \(5\) marbles each.

(iii) Product of number of marbles they now have is \(124.\)

What is Unknown?

Number of marbles John and Jivanti started with (each).

Reasoning:

Let the number of marbles that John had be \(x.\)

The number of marbles Jivanti had will be (Total marbles MINUS the Number of marbles John had) \(= 45-x\)

(i) Both of them lost \(5\) marbles each:

John \(= x-5\)

Jivanti \(=45 - x - 5 = 40 - x\)

(ii) Product of current number of marbles \(=124\)

\[\left( {x - 5} \right)\left( {40 - x} \right) = 124\]

Steps:

\[\begin{align}\left( {x - 5} \right)\left( {40 - x} \right) &= 124\\40x - {x^2} - 200 + 5x &= 124\\
 - {x^2} + 45x - 200 - 124 &= 0\\ - {x^2} + 45x - 324 &= 0\\{x^2} - 45x + 324 &= 0\\{x^2} - 36x - 9x + 324 &= 0\\x\left( {x - 36} \right) - 9\left( {x - 36} \right) &= 0\\\left( {x - 36} \right)\left( {x - 9} \right) &= 0\\x - 36 = 0 &\qquad x - 9 = 0\\x = 36 &\qquad x = 9\end{align}\]

John and Jivanti started with \(36\) and \(9\) marbles.

(ii)

What is known?

(i) Cost of each day is \(55\, –\) (number of toys produced in a day) rupees.

(ii) On a particular day the total cost of production was \(\rm{Rs.}\,750.\)

What is Unknown?

Number of toys produced on that day.

Reasoning:

Let the number of toys produced in a day is \(x.\)

(i) Cost of each toy \(= (55 - x)\) rupees

(ii) Total cost of production \(=\) Cost of each toy \(\times\) Total number of toys

\[\begin{align}(55 - x)(x) &= 750\end{align}\]

Steps:

\[\begin{align}(55 - x)(x) &= 750\\55x - x &= 750\\55x - x - 750 &= 0\\
x - 55x + 750 &= 0\\x - 25x-30x + 750 &= 0\\x(x - 25)-30\left( {x - 25} \right) &= 0\\
(x - 25)(x - 30) &= 0\\x-25 = 0 &\qquad x-30 = 0\\x = 25 &\qquad x = 30\end{align}\]

Number of toys produced on that day is \(25\) or \(30.\)

  
Learn math from the experts and clarify doubts instantly

  • Instant doubt clearing (live one on one)
  • Learn from India’s best math teachers
  • Completely personalized curriculum

Frequently Asked Questions



What are Class 10 NCERT Exemplars?
While getting good scores in school tests is a desirable outcome, it is not a reliable indicator of how strong your child’s math foundation really is. Many students who score well in school exams in their earlier years, might struggle with math in higher grades because of a weak foundation. At Cuemath, we evaluate your child’s grasp of math fundamentals, and take corrective actions immediately. Also, your child may have limited exposure in their school, and in most cases, may not feel challenged to learn more. Cuemath's customised learning plan ensures your child is challenged with varied difficulty levels of questions at every stage.
What is the difference between CBSE and NCERT syllabus for Class 10?
How will Class 10 NCERT books help in exam preparation?
How will Class 10 NCERT books help you understand basic math concepts?
Which is the best video solution for the class 10 maths NCERT?