Question

Three consecutive whole numbers are such that if they are divided by 5, 3 and 4 respectively; the sum of their quotients is 40. Find the numbers.
A. 20, 35 and 22
B. 50, 51 and 52
C. 40, 11 and 25
D. 5, 5 and 8

Answer 1

Hint: The three numbers are consecutive. So let the first number be x, the second number will be $ x + 1 $ and third number will be $ x + 2 $ . Quotient is the result of the division of two numbers. So add the divisions x by 5, $ x + 1 $ by 3 and $ x + 2 $ by 4 and equate it to 40.

Complete step-by-step answer:
We are given that three consecutive whole numbers are such that if they are divided by 5, 3 and 4 respectively; the sum of their quotients is 40. We have to find those numbers.
Let the numbers be x, $ x + 1 $ and $ x + 2 $ .
This means that $ \dfrac{x}{5} + \dfrac{{x + 1}}{3} + \dfrac{{x + 2}}{4} = 40 $
Finding the LCM of the LHS
 $ \Rightarrow \dfrac{{12x + 20\left( {x + 1} \right) + 15\left( {x + 2} \right)}}{{60}} = 40 $
 $ \Rightarrow \dfrac{{12x + 20x + 20 + 15x + 30}}{{60}} = 40 $
On cross multiplication, we get
  $ \Rightarrow 12x + 20x + 20 + 15x + 30 = 60 \times 40 = 2400 $
 $ \Rightarrow 47x + 50 = 2400 $
 $ \Rightarrow 47x = 2400 - 50 = 2350 $
 $ \therefore x = \dfrac{{2350}}{{47}} = 50 $
Therefore, the numbers are 50, $ 50 + 1 = 51,50 + 2 = 52 $ .
So, the correct answer is “Option B”.

Note: Another approach.
We are given that the three consecutive whole numbers are divided by 5, 3 and 4 respectively. This means that the three numbers must be in an increasing order and difference between any two of these three consecutive numbers must be 1. As we can see the options, in the first option 20, 35 and 22 are not in an increasing order and these are not consecutive numbers.
In Option C, 40, 11 and 25 are also not in an increasing order and these are definitely not consecutive whole numbers. In Option D, 5, 5 and 8; 5 is not the consecutive number of 5.
Therefore, Option B is correct as 50, 51 and 52 are consecutive and in an increasing order.