Question

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

Answer 1

Let the consecutive numbers be x , x+1, x+2According to the questionx/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 = 52i,e. 50,51,52

Answer 2

x/5 + x+1/5 + x+2/5 = 40-----------------> 12x+20x+15x+20+30=2400

47x + 50 = 2400------> x = 2350/47

x=50, x+1=51, x+2=52.