Let the original price of one mobile handset be denoted as $P$. The total amount Rakesh has is sufficient to buy 8 handsets at the original price, so his total amount is $8P$.

Calculate the Discounted Price:

• With the discount, Rakesh can buy 10 handsets. Therefore, the price per handset after the discount is $8P/10 = 0.8P$.

Determine the Discount Amount:

• The discount amount per handset is the difference between the original price and the discounted price:
• Discount per handset=$P - 0.8P = 0.2P$

Calculate the Discount Percentage:

• The discount percentage is the discount amount divided by the original price, multiplied by 100:

Discount percentage = $({0.2P \over P}) \times 100 = 20$%

Therefore, the retailer offered a 20% discount.