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

Question

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

Camila · Answer

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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