A certain number of apples, when attempted to be distributed to three groups in the ratio 3:4:5, fall short by one. If distributed in the ratio 4:5:6 two apples would be left undistributed. Which one of the following is a possible number of apples?

Correct option is B

Given:

In ratio 3:4:5 → apples fall short by 1
In ratio 4:5:6 → 2 apples are extra

Concept:

​We will convert the statements into mathematical expressions and then solve it.

Solution:

​According to the first statement, if the total number of apples is n, then

3x + 4x + 5x - 1 = n
12x - 1 = n

According to the second statement,

4y + 5y + 6y + 2 = n
15y + 2 = n

Comparing both the equations, we get:
12x - 1 = 15y + 2
=> 12x - 15y = 3
=> 4x - 5y = 1

Solving this, we find that x = 4 and y = 3 satisfies the equation.

So, number of apples = 12x - 1 = 12*4 - 1 = 47

Hence, number of apples is 47.