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 three consecutive whole numbers be x, x + 1 and x + 2

According to the statement:

`"x"/5 + ("x" + 1)/3 + ("x" + 2)/4 = 40`

`=> "x"/5 xx 60 + ("x" + 1)/3 xx 60 + ("x" + 2)/4 xx 60 = 40 xx 60`   ....[Multiplying each term by 60 because L.C.M. of denominators = 60]

⇒ 12x + 20(x + 1) + 15(x + 2) = 2400

⇒ 12x +20x + 20 + 15x + 30 = 2400

⇒ 12x + 20x + 15x = 2400 - 20 -30

⇒ 47x = 2350

⇒ x = `2350/47`

x = 50

x + 1 = 50+1 = 51

x + 2 = 50 + 2 = 52

Three consecutive whole numbers are 50, 51 and 52