Three water pumps operate at intervals of 6.25 minutes, 8.75 minutes and 12.5 minutes respectively. After how many minutes will they operate together again ?
87.5 minutes
The intervals can be written as fractions: \(6.25 = \frac{25}{4}\), \(8.75 = \frac{35}{4}\), and \(12.5 = \frac{50}{4}\) minutes.
The time when all three pumps operate together again is the LCM of these intervals, given by \(\text{LCM} = \frac{\text{LCM}(25, 35, 50)}{\text{HCF}(4, 4, 4)}\).
Since \(25 = 5^2\), \(35 = 5 \times 7\), and \(50 = 2 \times 5^2\), the LCM of 25, 35, and 50 is \(2 \times 5^2 \times 7 = 350\).
So the required LCM is \(\frac{350}{4} = 87.5\) minutes.
Hence, the three pumps will operate together again after 87.5 minutes.
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