Two balls A and B rotate along a circular track. Ball A makes 2 full rotations in 26 minutes. Ball B makes 5 full rotation in 35 minutes. If they start rotating now from the same point, when will they be at the same starting point again?
Correct answer: A
Explanation
If ball A makes 2 rotations in 26 minutes, it makes 1 rotation in 13 minutes. If ball B makes 5 rotations in 35 minutes, it makes 1 rotation in 7 minutes.
The two balls start rotating now and makes several rotations before they are at the SAME starting points. Ball A would have done a WHOLE number X of rotations and ball B would have done a WHOLE number Y of rotations. Also they would have rotated during the same period of time T. Hence
T = 13 X = 7 Y
Hence 13 X = 7 Y
Solve the above for X
X = 7 Y / 13
We want the time when they are FIRST at the same starting point. Therefore X and Y are the smallest whole numbers of the equation X = 7 Y / 13. The smallest value of Y that gives X as a whole number is 13. Hence
X = 7 (13) / 13 = 7
Time T is given by
T = 13 X = 13 * 7 = 91 minutes = 1 hour and 31 minutes
correct answer A
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AQuA-RAT items are crowdsourced algebra problems, not ACT questions. They carry five answer choices in the pre-2025 ACT Mathematics style and no ACT reporting category. Useful for drilling Preparing for Higher Math content; not a substitute for a real form.