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

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## 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
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 $$30.$$

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