The average of four numbers is 45. If 10 is added to the first number, the second number is multiplied by 5, 10 is subtracted from the third number, and the fourth number is divided by 5, all the results are equal. Find the difference between the second-highest number and the smallest number.

ATQ, Let the common resulting value be y. When 10 is added to the first number, the result is y. So, first number = y − 10 When the second number is multiplied by 5, the result is y. So, second number = y/5 When 10 is subtracted from the third number, the result is y. So, third number = y + 10 When the fourth number is divided by 5, the result is y. So, fourth number = 5y Average of four numbers = 45 So, total of four numbers = 45 × 4 = 180 Now add the four numbers: (y − 10) + y/5 + (y + 10) + 5y = 180 (2y) + 5y + y/5 = 180 7y + y/5 = 180 (35y + y)/5 = 180 36y/5 = 180 36y = 180 × 5 36y = 900 y = 900/36 y = 25 First number = 25 − 10 = 15 Second number = 25/5 = 5 Third number = 25 + 10 = 35 Fourth number = 5 × 25 = 125 Numbers are 15, 5, 35 and 125 Smallest number = 5 Second-highest number = 35 Required difference = 35 − 5 = 30