Question

11.
18
A shopkeeper buys certain goods. He sells one-third of them at 20% profit and three-eighth
of the remaining at 20% loss. What should be the mark-up on the remaining goods so that
after giving a discount of 20% on them while selling, the shopkeeper gets a profit of 10%
on overall transaction?
1) 50%
2) 40%
3) 25%
4) 20%​

Answer 1

Given : A shopkeeper buys certain goods. He sells one-third of them at 20% profit and three-eighth of the remaining at 20% loss. remaining at a discount of 20% on Marked price . shopkeeper gets a profit of 10%

on overall transaction

To find :   What should be the mark-up on the remaining goods

Solution:

Let say  Shopkeeper buys  12G   - goods

Cost price of each good = C

Total Cost Price = 12G * C = 12GC

10% Profit on over all transaction = (10/100)12GC = 1.2GC

Total Selling Price = 12GC + 1.2GC = 13.2GC

sells one-third of them at 20% profit  

=> Selling Price =  (1/3)12G  * C( 1 + 20/100)  = 4.8GC

remaining = 12 - (1/3)12G = 8G

(3/8) * 8G = 3G

Sold at loss of  20% loss

Selling Price =  3G * C(1 - 20/100) = 2.4GC

remaining item = 8G - 3G = 5G

Let say  Marked Price  = M

Price after  20% Discount   = M - (20/100)M = 0.8M

Selling Price = 5G * 0.8M =  4MG

4.8GC +  2.4GC + 4MG  = 13.2GC

=> 4MG  =  6GC

=> M = 3C/2

=> M - C = C/2

100* (C/2)/C = 50 %

There should be 50 % Markup at remaining goods

option 1 is correct

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