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Q.

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in Rs.) was found to be 55 minus the number of toys produced in a day. On a particular day, the cost of production was 750. If x denotes the number of toys produced that day, then what are the values of x?


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a

25 or 30

b

28 or 29

c

22 or 36

d

20 or 30 

answer is A.

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Detailed Solution

Given that the cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day.
Let the number of toys produced in a day = x.
Cost of production of each toy on the given day (in Rs.) = 55 – x.
Total cost of production on the given day (in Rs.) = x(55 – x).
According to the question, the total cost of production on the given day (in Rs.) = 750.
The equation formed will be
 x(55 – x) =750
⇒   55x− x 2 =750  
⇒   55x− x 2 −750=0  
⇒   x 2 −55x+750=0  
⇒   x 2 −25x−30x+750=0  
⇒   x(x−25)−30(x−25)=0  
Factoring the equation to get two linear factors, we have
⇒   x(x−25)−30(x−25)=0  
⇒(x−30)(x−25)=0 ⇒x−30=0 or x−25=0  
Thus, x=30 or x=25 are two roots of the equation x 2 −55x+750=0  
Therefore,  the correct option is 1.
 
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