Question

Dr. Stephen Strange bought two surgical instruments for Rs. 12300. He sold one at a profit of 33(1/3)% and the other at a loss of 33(1/3)%. If the selling price of both the instruments are same, then their cost prices are 
1. Rs. 7200 and Rs. 5100
2. Rs. 6000 and Rs. 6300
3. Rs. 4100 and Rs. 8200
4. Rs. 5200 and Rs. 7100

Answer 1

Correct Answer - Option 3 : Rs. 4100 and Rs. 8200

Given:

Cost price of both instruments = Rs. 12300

Profit on first instrument = 33(1/3)%

Loss on second instrument = 33(1/3)%

Formula Used:

Profit % = ((SP - CP)/CP) × 100%

Loss % = ((CP - SP)/CP) × 100%

Calculation:

Let the cost price of first instrument = Rs. x

and the cost prize of second instrument = Rs. y

Let the selling prize of each instrument = Rs. z

Profit on first instrument = 33(1/3)%

Profit % = ((SP - CP)/CP) × 100%

⇒ 33(1/3) = ((z - x)/x) × 100

⇒ 1/3 = (z - x)/x

⇒ x = 3(z - x)

⇒ x = 3z - 3x

⇒ 4x = 3z

⇒ x = (3/4)z

Loss on second instrument = 33(1/3)%

Loss % = ((CP - SP)/CP) × 100%

⇒ 33(1/3) = ((y - z)/y) × 100

⇒ 1/3 = (y - z)/y

⇒ y = 3(y - z)

⇒ y = 3y - 3z

⇒ 2y = 3z

⇒ y = (3/2)z

∵ x + y = 12300

⇒ (3/4)z + (3/2)z = 12300

⇒ (9/4)z = 12300

⇒ z = 16400/3

x = (3/4)z

⇒ x = (3/4) × (16400/3)

⇒ x = 4100

Cost price of first instrument = Rs. 4100

 y = (3/2)z

⇒ y = (3/2) × (16400/3)

⇒ y = 8200

Cost price of second instrument = Rs. 8200

∴ The cost price of both instruments are Rs. 4100 and Rs. 8200 respectively.