When a discount of 20% is given on a sweater, the profit is 28%. If the discount is 14%, then the profit is

Let the C.P. of sweater be Rs. 100 and its marked price be Rs. x. According to the question, $x imes frac{80}{100}=128$ $Rightarrow x imes frac{4}{5}=128$ $Rightarrow x=frac{128 imes 5}{4}=$ Rs. 160 When discount = 14%, then S.P. of sweater = 160 × (100 – 14)% $=frac{160 imes 86}{100}=$ Rs. $137.6$ ∴ C.P. = Rs. 100 ∴ Profit per cent = 37.6%

Alternative:

In this case. S.P. will be equal

M.P. (100 – Discount) = C.P. (100 + Gain)

M.P. (100 – 20) = C.P. (100 + 28)

$frac{mathrm{M} . mathrm{P} .}{mathrm{C.P.}}=frac{128}{80}$

In 2nd case,

14% discount on M.P.

S.P. = 14% of 128 – 128

= 128 – 17.92

= 110.08

∴ C.P.= 80, S. P. = 110.08

Gain $\%=frac{ ext { (S.P.-C.P.) } imes 100}{ ext { C.P. }}$

$=frac{110.08-80}{80} imes 100=frac{300.8}{8}=37.6 \%$