21 poles stand evenly spaced along a path. A car reaches the 16th pole in 30 seconds. How long to reach the final pole?
Show answer Hide answer
Answer: B. 40 seconds
Explanation
Twenty-one evenly spaced poles along a path create exactly twenty total intervals between the first and last pole. Reaching the sixteenth pole involves fifteen intervals, which take thirty seconds, meaning each interval takes two seconds. Multiplying the total of twenty intervals by the two seconds per interval rate yields a total time of forty seconds. Interval counting problems require recognizing that the number of spaces between objects is always one less than the object count. Uniform spacing allows problems to be solved by determining the exact time required to traverse a single interval unit. Rate calculations link physical distance intervals directly to elapsed time measurements in motion problems.
Option A suggests thirty-nine seconds, which miscalculates the final interval multiplication step. Option C proposes thirty-nine point thirty-eight seconds, introducing an unnecessary decimal fraction into the uniform rate. Option D offers thirty-nine point five seconds, failing to match the exact integer product of twenty intervals and two seconds.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. Four prime numbers in ascending order have a product of 385 for the first three and 1001 for the last three. Find the fourth number.
Show answer Hide answer
Answer: A. 5
Prime factorization of three eighty five reveals the first three prime numbers as five, seven, and eleven. Prime factorization of one thousand one yields seven, eleven, and thirteen as the last three primes. Arranging th...
Q2. A zoo has rabbits and peacocks totaling 60 heads and 192 legs. Find the total number of rabbits.
Show answer Hide answer
Answer: E. None of these
Setting up simultaneous equations for animal heads and total leg counts determines the exact rabbit population. Assuming forty-four rabbits and sixteen peacocks yields sixty total heads and one hundred ninety-two total l...
Q3. Three numbers exist where 5/7th of the first equals 48% of the second, and the second is 1/9th of the third. If the third is 1125, find 25% of the first.
Show answer Hide answer
Answer: D. 21
By working backwards from the third number (1125), the second is 125, the first is 140, and 25% of the first is 35, which is not listed, making 'None of these' correct.
Q4. A machine depreciates by 20% p.a. from a current value of Rs. 1,50,000. At what price should it be sold after two years to yield a Rs. 24,000 profit?
Show answer Hide answer
Answer: B. Rs. 1,20,000
Depreciating fifteen hundred thousand at twenty percent p.a. over two years reduces its value to ninety six thousand. Adding the target profit of twenty four thousand to the depreciated value gives one twenty thousand. T...
Q5. An item's price rises 30% in year one, drops 20% in year two, and climbs 10% in year three. If the final price is Rs. 2288, what was the initial price?
Show answer Hide answer
Answer: C. Rs. 2000
Representing the initial price as P allows setting up sequential percentage multipliers for each year. Multiplying the initial price by one point thirty, zero point eighty, and one point ten equals the final price. Solvi...
Q6. Three 6-sided dice are rolled simultaneously. What is the probability that all three display the same number-.
Show answer Hide answer
Answer: B. 1/36
Rolling three six-sided dice simultaneously produces a total sample space of two hundred sixteen outcomes. The number of favorable outcomes where all three dice show identical numbers is exactly six possible ways. Dividi...