GATE | GATE CS 2021 | Set 2 | Question 9

The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in Year 3 was Re. 1, which was half the cost/unit in Year 2. The cost/unit in Year 3 was one-third of the cost/unit in Year 1. Taxes were paid on the selling price at 10%, 13%, and 15% respectively for the three years. Net profit is calculated as the difference between the selling price and the sum of cost and taxes paid in that year.

The ratio of the selling price in Year 2 to the selling price in Year 3 is _________.
(A) 4:3
(B) 1:1
(C) 3:4
(D) 1:2


Answer: (A)

Explanation:

From the above graph we obtained following information- 

Year    Cost/Unit   Cost Price    Number of Units
1             3              300             100
2             2              400             200
3             1              300             300

Let selling price of year 2 = SP2 and Selling price of year3 = SP3

Given that-

Taxes for year 2 = 13% of SP2 = 0.13SP2
Taxes for year 3 = 15% of SP3 = 0.15SP3
Cost per unit of year 3 = 1
(Cost per unit of year 2)/2 = 1
So now Cost / unit of year 2 = 2*1 = 2

Net profit formula now = Selling Price – (Cost Price + (Tax% x selling price )

For year 2

296 = SP2- (200*2 + 0.13*SP2)
SP2 = 696*100/87
SP2 = 800

For year 3

210 = SP3 - (300*1+0.15*SP3)
SP3 = 510*100/85
SP3 = 600

Required Ratio 800/600= 4/3 (Correct Option A)

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