Each of the questions below consists of a question and two statements...
Let cost price of commodity be "c"
Marked price be "m"
Selling price be "s"
Profit percentage be "p%"
Discount percentage be "d%"
p/d = ½ ..................(i)
s = (1+ p/100)c .........(ii)
s= (1-d/100)m .........(iii)
Statement I
It says that the product was marked up by 50%
m = 1.5c
using (i), (ii) and (iii)
c+ pc/100 = m - md/100
p/100 (c + 2m) = m-c
or p = 0.5/4 x 100 = 12.5%
d= 25%
discount = 25/100 x m = ¼ x 1.5c = 0.375 c
s = (1+ 12.5/100)c
s=1.125c
Required % = discount/selling price x 100 = 0.375c/1.125c * 100 = 33.33%
Statement II
It says that total discount offered is four times total profit made.
So,
d/100 x m = 4 x p/100 x c
or m/c = 4 x p/d
m = 2c
using (i), (ii) and (iii)
c+ pc/100 = m - md/100
p/100 (c + 4c) = m-c
or p = 1/5 x 100 = 20%
d= 40%
discount = 40/100 x m = 4/10 x 2c = 0.8 c
s = (1+ 20/100)c
s=1.2c
Required % = discount/selling price x 100 = 0.8c/1.2c × 100 = 66.66%