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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?
- A70%
- B60%
- C50%
- D40%
Answer not set
Discussion 1
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CCommunity
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%
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%