# Solve the problems given in Example 1

**Solution:**

The problem in example 1 was as follows:

Represent the following situations mathematically:

(i) John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number 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.

Given:

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

The number of marbles Jivanti had will be = 45 - x

Both of them lost 5 marbles each:

Marbles with John = x - 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 be x.

Cost of each toy = (55 - x) rupees

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} - 25x - 30x + 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.

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 4

**Video Solution:**

## Solve the problems given in example 1

Class 10 Maths NCERT Solutions Chapter 4 Exercise 4.2 Question 2

**Summary:**

If John and Jivanti together have 45 marbles and both of them lost 5 marbles each, and the product of the number of marbles they now have is 124 then the number of marbles they had to start with is 9 and 36.

If a cottage industry produces a certain number of toys in a day and the cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day where, on a particular day, the total cost of production was ₹ 750, the number of toys produced on that day is 25 or 30.

**☛ Related Questions:**

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