Question 14 A number 240 is divided into 3 parts in the ratio 1 : 6 : 3.
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A number 240 is divided into 3 parts in the ratio 1 : 6 : 3.
What is the largest 3-digit number divisible by all of them?
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Answer: D. D) 864
The parts are 24, 144, and 72. Their LCM is 144. The largest 3-digit multiple of 144 is 864.
Step-by-step Derivation:
Step 1: Sum of ratio parts = 1 + 6 + 3 = 10.
Step 2: Parts are (1/10)*240 = 24, (6/10)*240 = 144, and (3/10)*240 = 72.
Step 3: Find LCM(24, 144, 72). Since 144 is divisible by 24 and 72, LCM = 144.
Step 4: Largest 3-digit multiple of 144 = floor(999 / 144) * 144 = 6 * 144 = 864.