The average temperature of a city in the first four days of a month was 36°.The average for the 2nd, 3rd, 4th and 5th day was 38°.If the temperature of the 1st and 5th day were in the ratio 4 : 5, then what is the temperature on the fifth day ?
Question
The average temperature of a city in the first four days of a month was 36°.The average for the 2nd, 3rd, 4th and 5th day was 38°.If the temperature of the 1st and 5th day were in the ratio 4 : 5, then what is the temperature on the fifth day ?
Solution
Step 1: Calculate the total temperature for the first four days. Since the average temperature for the first four days is 36°, the total temperature for these days is 36° * 4 = 144°.
Step 2: Calculate the total temperature for the second, third, fourth, and fifth days. Since the average temperature for these days is 38°, the total temperature for these days is 38° * 4 = 152°.
Step 3: Subtract the total temperature of the first four days from the total temperature of the second, third, fourth, and fifth days to find the temperature of the fifth day. This is because the fifth day is the only day not included in the total temperature of the first four days. So, the temperature of the fifth day is 152° - 144° = 8°.
Step 4: We know that the temperature of the first and fifth days were in the ratio 4:5. Let's denote the temperature of the first day as 4x and the temperature of the fifth day as 5x. According to the information from step 3, 5x = 8°.
Step 5: Solve the equation from step 4 to find the value of x. x = 8° / 5 = 1.6°.
Step 6: Substitute x = 1.6° into the equation for the temperature of the fifth day (5x) to find the actual temperature on the fifth day. The temperature on the fifth day is 5 * 1.6° = 8°.
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