profit and loss

[vaibhav101]

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 changes in January, the fixed cost of producing item X was 5 times the variable cost of producing item X

[deloitte247]

T= Total cost, F=Fund cost, V=Variable cost
Target question T=F+V
Statement 1 = Fixed cost charges 1.13, F =1.13
Total cost (T)= $$\frac{\left[\left(V+F\right)-\left(0.95V+1.13F\right)\right]}{\left(V+F\right)}$$
= $$\frac{\left(0.95V+1.13F\right)}{\left(V+F\right)}$$
No definite relationship between fixed and variable cost so we cannot calculate the value of T so statement 1 is not SUFFICIENT
Statement 2 $$F=5\cdot V$$
$$F=5V$$
The changes is fixed cost F is not known so we cannot calculate the value of T (Total cost) .Therefore statement 2 is not SUFFICIENT.

Combining statement 1 and 2 together. it gives a definite relationship between F and V and also individual % increase or decrease.
Hence statement 1 and 2 together is SUFFICIENT (answer is Option C )