Question : A and B have some toffees. If A gives one toffee to B, they will have an equal number of toffees. If B gives one toffee to A, the number of toffees with A is double the number with B. The total number of toffees with A and B is:
Option 1: 12
Option 2: 10
Option 3: 14
Option 4: 15
Correct Answer: 12
Solution :
Let the number of toffees with A and B be x and y respectively.
According to the question:
Case 1.
x – 1 = y + 1
⇒ x = y + 2...............(equation 1)
Case 2.
x + 1 = 2(y – 1)
⇒ x – 2y = –3....................(equation 2)
Putting the value of x, we get:
2 + y – 2y = –3
⇒ y = 5
Putting the value of y in equation 1, we get:
x = 5 + 2 = 7
Total toffees = 5 + 7 = 12
Hence, the correct answer is 12.
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