GATE CSE 2021 Set 2 | GA Question: 9

Question

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 ₹$\;1$, 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 1

Lets denote $\text{CP}_x$ and $\text{SP}_x$ for per unit Cost Price and Selling Price respectively for year $x.$ Given that

$ \frac{1}{3}\text{CP}_1  = \frac{1}{2}\text{CP}_2 = \text{CP}_3 =$ ₹$~1$

$\quad \implies \text{CP}_2 =$ ₹$~2,\text{CP}_3 =$ ₹$~1$

Net profit for year $2$ is given by

$\text{SP}_2 – (200*\text{CP}_2 + 0.13*\text{SP}_2) = 296 $      

$\quad \implies 0.87*\text{SP}_2 = 296 + 200*2 = 696$

$\quad \implies \text{SP}_2 = \frac{696}{0.87} =$ ₹$~800 \qquad \qquad \qquad \to (i)$

Net profit for year $3$ is given by
 
$\text{SP}_3 – (300*\text{CP}_3 + 0.15*\text{SP}_2) = 210 $

$\quad \implies 0.85*\text{SP}_3 = 210 + 300*1 = 510$

$\quad \implies \text{SP}_3 = \frac{510}{0.85} =$ ₹$~600  \qquad \qquad \qquad \to (ii)$

$(i)\div(ii) \implies \frac{\text{SP}_2}{\text{SP}_3} = \frac{800}{600} = \frac{4}{3}$  
 
Ans: A.  $4:3$

Comments

But isn't that revenue. Normally, SP and CP are told in terms of per unit.

Answer 2

Given that:

cost per unit of year 3=Rs.1

and Cost per unit of year 3=(cost per unit of year 2)/2

So, cost per unit of year 2=2*cost per unit of year 3

=2*1=2.

let selling price of year 2=sp2 and selling price of year 3=sp3.

 we have taxes in year 2 and 3 as 13% and 15% of selling price respectively.

Tax in year 2=13*sp2/100=.13*sp2

Tax in year 3=15*sp3/100=0.15*sp3

profit in year 2=selling price in year 2$-$(cost of all units +tax in year 2)

296=sp2$-$(200*2+0.13*sp2)

296=sp2$-$400$-$0.13sp2

296+400=0.87*sp2

696*100/87=sp2

sp2=800.

profit in year 3=selling price in year 3$-$(cost of all units +tax in year 3)

210=sp3$-$(300*1+0.15*sp3)

210=sp3$-$300$-$0.15sp3

210+300=0.85*sp3

510*100/85=sp3

sp3=600.

Ratio of selling price in year 2 to selling price in year 3

=800/600

=4/3