Option 3 : Rs. 10000

**Given:**

Cost price of both motorcycles = Rs. 60000

Profit on first motorcycle = 5%

Profit on second motorcycle = 47%

Selling price of first motorcycle = Selling price of second motorcycle

**Formula Used:**

Profit % = ((SP - CP)/CP) × 100%

**Calculation:**

Let the cost price of first motorcycle = Rs. x

and the cost price of second motorcycle = Rs. y

Let the selling price of each motorcycle = Rs. z

Profit on first motorcycle = 5%

Profit % = ((SP - CP)/CP) × 100%

⇒ 5 = ((z - x)/x) × 100

⇒ 1/20 = (z - x)/x

⇒ x = 20(z - x)

⇒ x = 20z - 20x

⇒ 21x = 20z

⇒ x = (20/21)z

Profit on second motorcycle = 47%

Profit % = ((SP - CP)/CP) × 100%

⇒ 47 = ((z - y)/y) × 100

⇒ 47y = 100(z - y)

⇒ 47y = 100z - 100y

⇒ 147y = 100z

⇒ y = (100/147)z

∵ x + y = 60000

∴ (20/21)z + (100/147)z = 60000

⇒ (5040/3087)z = 60000

⇒ z = 36750

∴ Selling price of each motorcycle = Rs. 36750

x = (20/21)z

⇒ x = (20/21) × 36750

⇒ x = 35000

y = (100/147)z

⇒ y = (100/147) × 36750

⇒ y = 25000

The cost price of two motorcycles was Rs. 35000 and Rs. 25000 respectively.

**∴ The difference of the cost price of the two motorcycles was Rs. 10000.**