Question

A shopkeeper marks his goods in such a way that after allowing a discount of 25% on the marked

price, he still makes a profit of 50%. Find the ratio of the C.P. to the M.P.
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Answer 1

Given,

Discount = 25%

Discount = (MP × Discount %)/100

= (MP×25)/100

= Rs 25MP/100

SP = MP – Discount

= (MP – 25MP/100)

= (100MP – 25MP)/100

= 75MP/100

We know that the given profit = 50%

Selling price = (100 + Gain %)/100 × CP

= (100 + 50)/100 × CP

= 150/100 × CP

= 150CP/100

By equating both SP we get,

75MP/100 = 150CP/100

75MP/150CP = 100/100

75MP/150CP = 1

(By cross multiplying)

CP/MP = 75/150

= 1/2

∴ The ratio CP to MP = 1:2

Answer 2

Given,

Discount = 25%

Discount = (MP × Discount %)/100

= (MP×25)/100

= Rs 25MP/100

SP = MP – Discount

= (MP – 25MP/100)

= (100MP – 25MP)/100

= 75MP/100

We know that the given profit = 50%

Selling price = (100 + Gain %)/100 × CP

= (100 + 50)/100 × CP

= 150/100 × CP

= 150CP/100

By equating both SP we get,

75MP/100 = 150CP/100

75MP/150CP = 100/100

75MP/150CP = 1

(By cross multiplying)

CP/MP = 75/150

= 1/2

∴ The ratio CP to MP = 1:2