Understanding House Intervals
The problem involves houses arranged in a row with equal spacing. The key is to determine the number of intervals between the houses, not just the number of houses.
- Total number of houses = 15.
- The number of equal intervals between 15 houses is \(15 - 1 = 14\).
Calculating Distance Per Interval
The total distance between the $1^{\text{st}}$ and $15^{\text{th}}$ house is given as 560 ft. This distance covers the 14 intervals.
Distance per interval = $ \frac{\text{Total Distance}}{\text{Number of Intervals}} $
Distance per interval = $ \frac{560 \text{ ft}}{14} = 40 \text{ ft} $.
Determining Distance Between 3rd and 7th House
We need to find the distance between the $3^{\text{rd}}$ and $7^{\text{th}}$ house. This involves houses from the $3^{\text{rd}}$ up to the $7^{\text{th}}$.
- The number of houses involved in this segment is $7 - 3 = 4$.
- The number of intervals between the $3^{\text{rd}}$ and $7^{\text{th}}$ house is $7 - 3 = 4$.
Distance = Number of intervals $\times$ Distance per interval
Distance = $4 \times 40 \text{ ft} = 160 \text{ ft}$.
Similar Questions
- The sum of the first 20 terms of the series $\frac{1}{5 \times 6} + \frac{1}{6 \times 7} + \frac{1}{7 \times 8} + \dots$ is:
- What is the sum of the squares of the numbers from 3 to 18?
Important Questions from Sequence & Series
4 is related to 64 following a certain logic. Following the same logic, 9 is related to 729. To which of the following is 12 related following the same logic?
(NOTE: Operations should be performed on whole numbers without breaking down the numbers into their constituent digits. E.g., 13 – Operations on 13 such as adding/multiplying, etc., to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)What should come in place of ? in the given series based on the English alphabetical order?
ACE, FHJ, KMO, PRT, ?
Which of the following numbers will replace the question mark (?) in the given series?
3, 17, 83, 329, ?, 1961
Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
Find the area (in cm²) of the sector, where the radius of the circle is 24 cm and length of the arc is 7 cm.
