XAT 2011 Question 97

Instructions

Answer questions based on the following information:
Mulchand Textiles produces a single product of only one quality – waterproof synthetic fabric. Mr.Sharma, the cost accountant of Mulchand Textiles, estimated the costs of Mulchand Textiles for different possible monthly output levels. Before he could tabulate his estimates his computer crashed, and Mr. Sharma lost all data. Fortunately he had some printouts of some incomplete tables, charts and diagrams. The table titled “Variable Cost Estimates of Mulchand Textiles” provided the estimates of labour and material costs.


Apart from labour and material costs Mulchand Textiles incurs administrative costs of Rs. 40,000 per month, and electricity costs. Mr. Sharma recalled that estimate data of variable electricity cost had certain peculiar characteristics. Values at every 25000 sq ft of output increased in geometric progression till 150000 sq ft of output, after which values increased in arithmetic progression for every 25000 sq ft of output. Mr. Sharma remembered that the electricity cost was estimated to be Rs. 3800 for 25000 sq.ft. of output, Rs. 5700 for 50000 square feet of output and Rs. 38856.50 for 175000 square feet of output.

Question 97

Mr. Sharma found some printouts of line diagrams. The axes of the graphs were not marked, but Mr. Sharma remembered that he measured monthly output on the x - axis. Which of the following diagrams would represent the estimates of electricity cost per square feet of output versus monthly output?

Solution

It is given that cost for electricity changed in geometric progression till 150000 sq ft. 

Estimated electricity cost for 25000 sq. ft = Rs. 3800

Estimated electricity cost for 50000 sq. ft = Rs. 5700

Hence, we can say that common ratio of the GP that is formed by electricity cost = $$\dfrac{5700}{3800}$$ = 1.5 

Therefore, estimated electricity cost for 75000 sq. ft = 5700*1.5 = Rs. 8550.

Similarly, we can calculate the electricity cost till 150000 sq. ft. 

Estimated electricity cost for 200000 sq. ft = 2*Estimated electricity cost for 175000 sq. ft - Estimated electricity cost for 150000 sq. ft = 2*38856.5 - 28856.25 = Rs. 48856.75 {As these numbers are in an arithmetic sequence).

Electricity cost per sq. ft. for 25000 sq. ft = $$\dfrac{3800}{25000}$$ = Rs. 15 

Similarly, we can calculate the remaining data.Tabulating the all data,

We can see from the table that the cost per sq. ft decreased first then increased to 0.24 which is present in option B. Hence, option B is the correct answer. 



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