A trader bought two articles for Rs. 490. He sold one at a loss of 20% and the other at a profit of 16%. If the selling price of both the articles is same, then the cost price (in Rs.) of the article sold at 20% loss will be:

A. 300

B. 280

C. 310

D. 290

SSC CGL 2022 13 August 2021 Shift 1

Solution:

Let the articles be A1 and A2 sold at 20% loss and 16% profit respectively.

Let the Cost Price (CP) of the A1 for the trader be = x

Then the Cost Price (CP) of the A2 for the trader will be = 490 - x

It is given that the Selling Price (SP) of A1 and A2 are the same.

Let the Selling Price be = y

It is given that,

On sale of A1, Loss % = 20%

On sale of A2, Profit % = 16%

We know that,

Loss % = ((CP - SP)/CP) * 100 .......(1)

Profit % = ((SP - CP)/CP) * 100 ........(2)

Putting values in eq. 1 for A1 and in eq. 2 for A2

20 = ((x - y)/x) * 100 .......(3)

16 = ((y - (490 - x))/(490 - x)) * 100 ....(4)

From eq. 3, we get

20/100 = 1 - y/x

y/x = 1 - 20/100

y/x = 80/100

y = 4x/5 ....(6)

Substitute eq. (5) in eq. (4)

16 = ((4x/5 - (490 - x))/(490 - x)) * 100

16/100 = (4x/5)/(490 - x) - 1

4x/(5(490 - x)) = 16/100 + 1

4x/(5(490 - x)) = 116/100

4x/(5(490 - x)) = 29/25

100x = 29 * 5 * (490 - x)

100x = 71050 - 145x

245x = 71050

x = 71050/245

x = 290.

Hence, (d) is the correct answer.

Percentage shortcuts for fast calculation.


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