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2026
X, Y and Z jump forward 4', 6' and 5', respectively. At 8 AM, they all land on mark 199'. How many times will they all land on the same mark (need not be at the same moment) between mark 195' and 1000', if all of them cross mark 1000' by 9 AM?

Explanation

X, Y, and Z jump forward in a repeating cycle of 4', 6', and 5' respectively, which means they land on marks that are multiples of 4, 6, and 5. The least common multiple (LCM) of these jumps (LCM of 4, 6, and 5) is 60. They all first land together at 199' and will next meet at every 60' interval thereafter. The marks they will land on between 195' and 1000' are calculated as: 240', 300', 360', 420', 480', 540', 600', 660', 720', 780', 840', 900', 960', and 1020', yielding 14 valid crossings in that range before exceeding 1000'.

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X, Y and Z jump forward 4', 6' and 5', respectively. At 8 AM, they all land on mark 199'. How many t — CSAT 2026 Answer & Explanation | UPSC Setu