A person allows 10% discount for cash payment from the marked price of a toy and still he makes a 10% gain. What is the cost price of the toy which is marked Rs 770?

Correct Option (3)

The problem requires determining the Cost Price (CP) of a toy given its Marked Price (MP), the discount offered, and the percentage gain achieved.

• The Marked Price (MP) of the toy is Rs 770.
• A 10% discount is provided for cash payment. The discount amount is calculated as:

  Discount = (10/100) * 770 = Rs 77.

• The Selling Price (SP) of the toy after applying the discount is:

  SP = MP - Discount = 770 - 77 = Rs 693.

• The person makes a 10% gain on the Cost Price (CP). Let the Cost Price be 'x'. The Selling Price can also be expressed in terms of CP and gain:

  SP = CP + (Gain % of CP)

  SP = x + (10/100)x

  SP = (11/10)x.

• By equating the two expressions for the Selling Price:

  (11/10)x = 693

  x = 693 * (10/11)

  x = 63 * 10

  x = 630.

• Therefore, the Cost Price of the toy is Rs 630.

Incorrect Options:

Options 1 (Rs 610), 2 (Rs 620), and 4 (Rs 640) are incorrect. If any of these values were the Cost Price, the resulting Selling Price after a 10% gain would not be consistent with the Selling Price derived from a 10% discount on the Marked Price of Rs 770, as established by the correct calculation.