A man bought 60 rings for Rs.
x. Out of total rings, 18 rings are damaged and the remaining are undamaged. 50% of the damaged rings are sold at a loss of 10% and the remaining damaged rings are sold at a loss of 20%. The undamaged rings are sold at a profit of 20%. If the total selling price of all the rings is Rs. (x + 57), then find the cost price of each ring.

ATQ, Cost price of one ring = x/60 Damaged rings = 18 50% of damaged rings = 9 So, 9 rings sold at 10% loss ⇒ SP = 9 × (x/60) × 90/100 9 rings sold at 20% loss ⇒ SP = 9 × (x/60) × 80/100 Undamaged rings = 60 − 18 = 42, sold at 20% profit ⇒ SP = 42 × (x/60) × 120/100 According to the question, 9 × (x/60) × 90/100 + 9 × (x/60) × 80/100 + 42 × (x/60) × 120/100 = x + 57 Or, 9 × (x/60) × 9/10 + 9 × (x/60) × 4/5 + 42 × (x/60) × 6/5 = x + 57 Or, 27x/200 + 3x/25 + 21x/25 = x + 57 Or, 27x/200 + 24x/200 + 168x/200 = x + 57 Or, 219x/200 = x + 57 Or, 219x = 200x + 11400 Or, 19x = 11400 So, x = 600 Cost price of one ring = x/60 = 600/60 = Rs. 10