The amount charged by a logistics company consists of two costs

Question

The amount charged by a logistics company consists of two costs, the fixed cost and the variable cost. The fixed cost is charged monthly and is the same for each month. The variable cost is directly proportional to the weight of the goods shipped. A merchant uses the company to ship 10 kg of goods in one month and 20 kg of goods in another month. Had he shipped all the goods in the same month, he would have saved 20% of his money. Find the ratio of fixed cost and the variable cost for 15 kg of goods all shipped in the same month.

A. 1:2
B. 2:3
C. 3:4
D. 4:5
E. 5:6

(adapted from gmatfree)

A. 1:2
B. 2:3
C. 3:4
D. 4:5
E. 5:6

(adapted from gmatfree)

TheAlchemist36 · Answer

Let fixed cost=100 and Variable cost/kg=v
Case 1: 
Month 1 cost= 100+10v
Month 2 cost= 100+20v
Total cost= 200 +30v
Case 2: All goods sent together in a single month
 Total cost = 100+30v
So,  100+30v= \frac{80}{100}(200+30v) 
Solving, v=10
So  \frac{Fixed cost}{Variable cost(for 15 kg)}= \frac{100}{150} 
 =2:3

The amount charged by a logistics company consists of two costs

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