# Solve the problems given in Example 1

**Solution:**

Given:

(i) a. John and Jivanti together had 45 marbles

b. Both of them lost 5 marbles

c. Product of the number of marbles they now have is 124.

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

Both of them lost 5 marbles each:

Marbles with John = - 5

Marbles with Jivanti = 45 - x - 5 = 40 - x

Product of current number of marbles = 124

Let us use this condition to form a quadratic equation.

(x - 5) (40 - x) = 124

(i) (x - 5) (40 - x) = 124

⇒ 40x - x^{2} - 200 + 5x = 124

⇒ -x^{2} + 45x - 200 -124 = 0

⇒ -x^{2} + 45x - 324 = 0

On multiplying both sides of the equation with negative sign, we get

⇒ x^{2} - 45x + 324 = 0

⇒ x^{2} - 36x - 9x + 324 = 0

⇒ x(x - 36) - 9 (x - 36) = 0

⇒ (x - 36) (x - 9) = 0

⇒ x - 36 = 0 and x - 9 = 0

⇒ x = 36 and x = 9

John and Jivanti started with 36 and 9 marbles.

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

a. Cost of each toy = (55 - x) rupees

b. Total cost of production = cost of each toy × Total number of toys

⇒ (55 - x) (x) = 750

⇒ 55x - x^{2} = 750

⇒ 55x - x^{2} + 750 = 0

⇒ x^{2} - 25 - 30 x + 750 = 0

⇒ (x - 25) (x - 30) = 0

x - 25 = 0 and x - 30 = 0

x = 25 and x = 30

The number of toys produced on that day is 25 or 30.

**Video Solution:**

## Solve the problems given in example 1

### Class 10 Maths NCERT Solutions- Chapter 4 Exercise 4.2 Question 2

Solve the problems given in example 1

The number of marbles they had to start with is 36 and 9 if John and Jivanti had 45 Both of them lost 5 marbles each and the product of the no. of marbles they now have is 124

The number of toys produced on that day is 25 or 30 if 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