Percentages

[MI3]

The total cost of producing item X is equal to the sum of item X's fixed cost and variable cost. If the variable
cost of producing X decreased by 5% in January, by what percent did the total cost of producing item X
change in January?
(1) The fixed cost of producing item X increased by 13% in January.
(2) Before the changes in January, the fixed cost of producing item X was 5 times the variable cost of
producing item X.

Answer provided is C , but I am not clear on the concept.. Can someone please assist?

Mant thanks.

[abhi0697]

Let T=total cost; F=fixed cost; V=variable cost
After change in January - T1=new total cost; F1=new fixed cost; V1=new variable cost

T=F+V; & V1=0.95*V

(1) F1=1.13*F
therefore, T1=F1 + V1 = 1.13*F + 0.95*V, we cannot solve this equation in terms of T alone. So IS

(2) F=5*V;
therefore, T1=F1 + V1= F1 + 0.95*V; we cannot solve this equation in terms of T alone. So IS

Combine (1) and (2); T1=F1 + V1= 1.13*F + 0.95*V=1.13*5*V + 0.95*V
& T = F + V = 5*V + V = 6*V

So, T1 = (1.13*5+0.95)*V = (1.13*5+0.95)*(T/6)

Hence, C

[Anurag@Gurome]

The total cost of producing item X is equal to the sum of item X's fixed cost and variable cost. If the variable
cost of producing X decreased by 5% in January, by what percent did the total cost of producing item X
change in January?
(1) The fixed cost of producing item X increased by 13% in January.
(2) Before the changes in January, the fixed cost of producing item X was 5 times the variable cost of
producing item X.


Answer provided is C , but I am not clear on the concept.. Can someone please assist?

Mant thanks.

Solution:
Let the fixed cost be 'f' and let the variable cost be 'v'.
So, the total cost is 'f + v'.
The variable cost decreases by 5% in January.
But we need to know more about fixed cost.
Let us first consider (1) alone.
If the fixed cost is increasing by 13% in January, the percentage change is
{(13/100)*f - (5/100)*v}/(f+v) * 100.
Obviously, this is not enough to answer the question.
So, (1) alone is not sufficient.
Next, consider (2) alone.
This means that f = 5v.
But nothing has been mentioned about the changes.
Or, (2) alone is not sufficient.
Next, combine both the statements together and check.
On combining, the % change is given by (65/100 * v - 5/100 * v)/6v * 100 = 10%.
So, both statements together are sufficient.

The correct answer is (C).

[Carcass]

I can't grasp the 2 statements combine an help ???