Three boys had a few coffee Bite toffees with them. The number of toffees with the second were four more than those with the first and the number of toffees with the third were four more than those with the second. How many toffees were there in all? I. The number of toffees with each of them is a multiple of 2. II. The first boy ate up four toffees from what he had and the second boy ate up six toffees from what had and the third boy gave them two toffees each from what he had and the number of toffees remaining with each of them formed a geometric progression.
Explanation:
Let the number of toffees with the first, second and third boy be x, (x+4) and (x+8) respectively. Hence, total number of toffees = (3x+12)
The statement I merely suggests that (3x+12) is a multiple of 2, which means that x is a multiple of 2. Nothing concrete can be concluded on the basis of this statement. The statement II suggests that (x – 4 + 2 ), (x + 4 –6 + 2) and (x + 8 – 4) are in GP or (x-2), x and (x+4) is in GP. ∴ x2 = (x + 4)(x − 2) ⇒ x = 4 ⇒ (3x + 12) = 24 Question can be answered using statement II alone.
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