Question

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.

Class 10 - Math - Quadratic Equations Page 76

Answer 1

Solution:

i)
Given John and jivanti together have 45 marbles

Let the number of Marbles John had be= x

Then the number of marbles jivanti had= 45-x

Both of them lost 5 Marbles each
Therefore, the number of marbles John had= x-5

The number of marbles jivanti had= 45-x-5= 40-x

Now product of the number of Marbles =124
Therefore , (x-5)(40-x)=124

40- x²-200+5x=124

-x²+45x-200-124=0

x² -45x+324=0. (Multiplying by(-1))

By factorisation method

x²-36x-9x+324=0

x(x-36) - 9(x-36)=0

(x-36)(x-9)=0

x=36 or x= 9

When John has 36 Marbles and jivanti has = 45-x= 45-36=9 marbles

When John has 9 Marbles and jivanti has= 45-x= 45- 9= 36 marbles

ii) Let the number of toys produced on that day be x.

Therefore the cost of production of each toy that day= 55 - x

So the total cost production that day=number of toys× cost of production of each toy that day

Total cost of production of toy=
x × (55-x)


A.T.Q..

x(55-x)=750

55x -x²= 750

-x²+55x-750=0

x²-55x+750=0

x²- 30x -25x+750=0

x(x-30)-25(x-30)=0


(x-30)(x-25)=0

x-30=0
x=30

x-25=0
x=25

Hence, the number of toys produced= x=25 or 30



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Hope this will help you..

Answer 2

Step-by-step explanation:

Pls refer the given answer