Anna and Ben each have a collection of marbles. If Anna gives one marble to Ben, they will both have an equal number of marbles. Conversely, if Ben gives one marble to Anna, she will end up with three times the number of marbles that Ben has. What is the total number of marbles they both have?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 8.
The number of marbles of Anna = A
The number of marbles of Ben = B
So, A - 1 = B + 1
⇒ A - B = 2 .....(1)
A + 1 = 3(B - 1)
⇒ A + 1 = 3B - 3
⇒ A - 3B = -4 .....(2)
Subtracting (2) from (1),
2B = 6
⇒ B = 6/2 = 3
Putting the value of B in (1),
A - 3 = 2
⇒ A = 2 + 3 = 5
Now, A + B = 5 + 3 = 8
Therefore, Annu and Ben both have 8 marbles.