A number is first decreased by 15% and then increased by 20%. The number so obtained is 78 more than the original number. The original number is: 

Let the original number be x. Decrease by 15% After 15% decrease, the number becomes: x - 15% of x = x - 0.15x = 0.85x Increase this result by 20% After 20% increase, the number becomes: 0.85x + 20% of 0.85x = 0.85x + 0.20 * 0.85x = 0.85x * (1 + 0.20) = 0.85x * 1.20 = 1.02x Use the given condition This final number is 78 more than the original number: 1.02x = x + 78 Step 4: Solve for x 1.02x - x = 78 0.02x = 78 x = 78 / 0.02 x = 78 * 100 / 2 x = 7800 / 2 x = 3900 Answer: 3900