A retailer made a profit when he allowed discount of 4% on the List Price of an item, but he incurred a loss to the extent of half of the rate percent of his profit when he raised the discount by 200%. What was his original profit percentage?
Options: 1)100/11 .2)100/13 .3)100/9 .4)100/17
Answers
Solution :-
→ Let MP of item = Rs.100
→ Discount = 4% .
so,
→ SP = MP * (100 - D)/100 = (100 * 96)/100 = Rs.96 .
Now, let profit is y% .
so,
→ CP = SP * 100 / (100 + profit)% = Rs.(96 * 100) / (100 + y) = Rs.(9600)/(100 + y)
again,
→ Let MP of item = Rs.100
→ Discount = 8% (4% raised by 200%)
so,
→ SP = MP * (100 - D)/100 = (100x * 92)/100 = Rs.92.
then,
→ Loss = CP - SP = [(9600)/(100 + y)] - 92 = (9600 - 9200 - 92y) / (100 + y) = Rs.(400 - 92y)/(100 + y)
therefore,
→ Loss % = (Loss * 100) / CP .
A/q,
→ [(400 - 92y)/(100 + y) * 100] / [(9600)/(100 + y) = (y/2)
→ 100(400 - 92y)/9600 = (y/2)
→ 40000 - 9200y = 4800y
→ 40000 = 4800y + 9200y
→ 40000 = 14000y
→ y = 40/14 = (20/7)% .
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