Three numbers in a 3:4:5 ratio have an L.C.M of 2400. Find their H.C.F:
Show answer Hide answer
Answer: A. 40
Explanation
Numbers in a three to four to five ratio can be expressed as three h, four h, and five h where h is their highest common factor. The least common multiple of numbers in this ratio is calculated by multiplying the ratio terms together with their common factor h. Setting sixty h equal to two thousand four hundred yields an HCF value of forty. The highest common factor is the largest positive integer that divides evenly into all numbers in a given set without remainders. The least common multiple of a set of proportional numbers is equal to the product of their ratio terms multiplied by their HCF. Ratio variables simplify the process of finding greatest common divisors and least common multiples for algebraic sets.
Option B suggests eighty, which yields an LCM exceeding the required two thousand four hundred threshold. Option C proposes one hundred twenty, creating a least common multiple far too large for the ratio terms. Option D offers two hundred, which produces a massive LCM that violates the problem parameters.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. Three colored flags permit generating codes via: I. A single flag, II. Any two flags in sequence, III. Three flags in sequence. What is the maximum number of codes.
Show answer Hide answer
Answer: C. 15
Generating codes using a single flag provides three distinct options based on the available inventory. Forming sequences of two flags gives three times two equal to six possible arrangements. Arranging three flags in seq...
Q2. Three standard dice (each marked with faces numbered 1 through 6) are rolled. How many outcome combinations exist where at least one die displays the digit 2?
Show answer Hide answer
Answer: C. 91
Rolling three standard dice generates a total sample space of two hundred sixteen possible outcomes. Calculating outcomes containing no digit two involves cubing five non matching faces to get one twenty five. Subtractin...
Q3. The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160. What is the time period:
Show answer Hide answer
Answer: D. 10 months
True discount represents the simple interest on the present worth of a bill due at a future date. Subtracting the true discount of one hundred sixty from the bill amount gives a present worth of sixteen hundred. Applying...
Q4. Reducing a commodity's tax by 20% while increasing its consumption by 10% results in what percentage decrease in revenue?
Show answer Hide answer
Answer: D. 12%
Tax reduction of twenty percent is represented by a multiplier of zero point eight. Consumption increase of ten percent is represented by a multiplier of one point one. Multiplying zero point eight by one point one gives...
Q5. Three mutually co-prime numbers have the product of the first two as 551 and the last two as 1073. What is their sum________?
Show answer Hide answer
Answer: C. 85
Factoring the product of the first two numbers reveals nineteen and twenty nine as prime factors. Factoring the product of the last two numbers yields twenty nine and thirty seven as prime factors. Identifying the shared...
Q6. Three pipes A, B, and C fill a tank in 6 hours. After 2 hours together, C is closed, and A and B finish the rest in 7 hours. How many hours does C need alone?
Show answer Hide answer
Answer: C. 14
Pipes A, B, and C combined complete one-sixth of the tank capacity per hour of operation. After working together for two hours, they complete one-third, leaving two-thirds of the tank remaining. Subtracting the combined...