By mistake, by dividing Rupees 2256 between x, y and z

Solution

Correct proportion = 1/3 : 1/4 : 1/5 LCM of 3, 4 and 5 = 60 So, correct ratio = 20 : 15 : 12 Total parts = 20 + 15 + 12 = 47 Total amount = Rs. 2256 Value of 1 part = 2256 ÷ 47 = Rs. 48 So, correct shares are: x = 20 × 48 = Rs. 960
y = 15 × 48 = Rs. 720
z = 12 × 48 = Rs. 576 Now, the amount was wrongly divided in the ratio 3 : 4 : 5 Total parts = 3 + 4 + 5 = 12 Value of 1 part = 2256 ÷ 12 = Rs. 188 So, wrongly divided shares are: x = 3 × 188 = Rs. 564
y = 4 × 188 = Rs. 752
z = 5 × 188 = Rs. 940 Now, Loss of x = 960 - 564 = Rs. 396 Gain of y = 752 - 720 = Rs. 32 Gain of z = 940 - 576 = Rs. 364 So, the one who loses the most = x = Rs. 396 loss
The one who gains the most = z = Rs. 364 gain Required difference = 396 - 364 = Rs. 32