Question

three consecutive whole numbers are such that if they be divided by 5,3and 4 respectively ;the sum of the quotients is 40 find the numbers.

Answer 1

Let the consecutive numbers be x , x+1, x+2
According to the question
x/5  + (x+1)/3  + (x+2)/4 = 40
⇒ [12x+ 20(x+1) + 15(x+2)]/60 = 40
⇒ [12x + 20x + 20 + 15x + 30]/60 = 40
⇒ [47x + 50]/60 = 40
⇒  47x + 50 = 40 × 60
⇒  47x + 50 = 2400
⇒  47x = 2400 - 50
⇒  47x = 2350
⇒  x = 2350/47
∴  x = 50
∴ The numbers are x= 50, x+1 = 51, x+2 = 52
i,e. 50,51,52