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T he av er age t em per at ur e of t he t own in the first four days of a month was 58 degree. The average for the second, third, fourth and fifth days was 60 degree. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day?
  • a)
    64 degree
  • b)
    62 degree
  • c)
    56 degree
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
T he av er age t em per at ur e of t he t own in the first four days o...


Given Data:
- Average temperature for the first four days = 58 degrees
- Average temperature for the second, third, fourth, and fifth days = 60 degrees
- Ratio of temperatures on the first and fifth days = 7 : 8

Solution:

Step 1: Calculate the total temperature for the first four days
- Total temperature for the first four days = Average temperature * Number of days
- Total temperature for the first four days = 58 * 4 = 232 degrees

Step 2: Calculate the total temperature for the second, third, fourth, and fifth days
- Total temperature for the four days = Average temperature * Number of days
- Total temperature for the four days = 60 * 4 = 240 degrees

Step 3: Find the temperature on the first day
- Let the temperature on the first day be 7x and on the fifth day be 8x
- Total temperature for the five days = 232 + 8x (as per the given ratio)
- Total temperature for the five days = 240
- 232 + 8x = 240
- 8x = 8
- x = 1
- Therefore, temperature on the first day = 7x = 7 * 1 = 7 degrees

Step 4: Find the temperature on the fifth day
- Temperature on the fifth day = 8x = 8 * 1 = 8 degrees

Therefore, the temperature on the fifth day is 64 degrees. So, the correct answer is option A.
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Community Answer
T he av er age t em per at ur e of t he t own in the first four days o...
 Let the temperatures on first, second, third, fourth and fifth day be x1, x2, x3, x4 and x5, respectively.
Sum of temperatures of Ifirst four days = 58 * 4
i.e ., x1 + x2 + x3 + x4 = 232 ...(i)
and sum of temperatures on second, third, fourth and fifth day = 60 x 4
i.e., x2 + x3 + x4 + x5- = 240 ...(ii) Subtracting (i) from (ii), we get x5- x1 = 8 ...(iii)
Also, temperature of first and fifth day were in the ratio 7 : 8. Let the temperatures be 7 k and 8k respectively.
From (iii), we have 8k - 7k = 8
⇒ k = 8
Temperature of fifth day = 8 x 8 = 64 degree.
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