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.
Answer:
(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.
∴ (x – 5) (40 – x) = 124
⇒ x2 – 45x + 324 = 0
⇒ x2 – 36x – 9x + 324 = 0
⇒ x(x – 36) −9 (x – 36) = 0
⇒ (x – 36) (x – 9) = 0
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
∴ x(55 – x) = 750
⇒ x2 − 55x + 750 = 0
⇒ x2 – 25x – 30x + 750 = 0
⇒ x(x – 25) – 30 (x – 25) = 0
⇒ (x – 25) (x – 30) = 0
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.
Latest Govt Job & Exam Updates: