NCERT MATHS CLASS - X
Quadratic Equations
Quadratic Equations
Exercise 4.2
Question 2:
(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. 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 Rs 750. Find out the number of toys produced on that day.
Sol.
(i) Let the number of John’s marbles be x.
Therefore, number of Jivanti’s marble = 45 − x
After losing 5 marbles,
Number of John’s marbles = x − 5
Number of Jivanti’s marbles = 45 − x − 5 = 40 − x
It is given that the product of their marbles is 124.
Either x ─ 36= 0 or x − 9 = 0
i.e., x = 36 or x = 9
If the number of John’s marbles = 36,
Then, number of Jivanti’s marbles = 45 − 36 = 9
If number of John’s marbles = 9,
Then, number of Jivanti’s marbles = 45 − 9 = 36
(ii) Let the number of toys produced be x.
Cost of production of each toy = Rs (55 − x)
It is given that, total production of the toys = Rs 750
Either x ─ 25 = 0 or x − 30 = 0
i.e., x = 25 or x = 30
Hence, the number of toys will be either 25 or 30.
Question 3:
Find two numbers whose sum is 27 and product is 182.
Let the first number be x and the second number is 27 − x.
Therefore, their product = x (27 − x)
It is given that the product of these numbers is 182.
Either x ─ 13= 0 or x − 14 = 0
i.e., x = 13 or x = 14
If first number = 13, then
Other number = 27 − 13 = 14
If first number = 14, then
Other number = 27 − 14 = 13
Therefore, the numbers are 13 and 14.
Question 4:
Find two consecutive positive integers, sum of whose squares is 365.
Let the consecutive positive integers be x and x + 1.
Either x + 14 = 0 or x − 13 = 0, i.e., x = −14 or x = 13
Since the integers are positive, x can only be 13.
x + 1 = 13 + 1 = 14
Therefore, two consecutive positive integers will be 13 and 14.
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