A trader allows a trade discount of 20% and a cash discount of 6¼% on the marked price of the goods and gets a net gain of 20% on the cost. By how much above the cost should the goods be marked for the sale?

A trader allows a trade discount of 20% and a cash discount of 6¼% on the marked price of the goods and gets a net gain of 20% on the cost. By how much above the cost should the goods be marked for the sale?

Let the marked price be x.

Now with a discount of 20%,

S.P = x – 20% of x

S.P = 80x/100

Other discount of 6¼ = 6.25% is provided

Hence, S.P = 80x/100 – 6.25% of 80x/100

S.P = 80x/100 - 5x/100

S.P = 75x/100

Given that this discount on the marked price leads to 20% gain on C.P.

Therefore,

75x/100 = C.P + 20/100 C.P

75x/100 = 120C.P/100

Hence, x = 120/75 C.P

Now increase in actual cost price, y = Marked price – C.P

y = 120/75 C.P – C.P

y = 45/75 C.P

In percentage,

Mark up% = (45/75 C.P)/C.P × 100

Mark up % = 45 × 100/75

Mark up % = 60%

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