Question

The average temperature of the town in the first four days of a month was 58 degrees. The average for the second, third, fourth and fifth day was 60 degrees. If the temperatures of the first and fifth day were in the ratio 7:8. Then what is the temperature on the fifth day?

• A. $64$ degrees
• B. $62$ degrees
• C. $56$ degrees
• D. None of these

Answer 1

The correct option is A $64$ degrees

Let the temperatures on five days be $x_1,x_2,x_3,x_4,x_5$

Given that the average temperature of the first four days is $58$ degrees.

Therefore, $58=\frac{x_1+x_2+x_3+x_4}{4}$

$⟹x_1+x_2+x_3+x_4=58\times 4=232$

$⟹x_2+x_3+x_4=232-x_1$ ------(1)

Given that average for the second, third, fourth and fifth days is $60$ degrees.

Therefore, $60=\frac{x_2+x_3+x_4+x_5}{4}$

$⟹x_2+x_3+x_4+x_5=60\times 4=240$ ------(2)

substituting (1) in (2) we get

$232-x_1+x_5=240$

$x_5-x_1=8$ -------(3)

Given that ratio of first-day and the fifth-day temperature is $7:8$

Therefore, $x_1:x_5=7:8$

$⟹x_1=\frac{7}{8}{x}_5$ ------(4)

substituting (4) in (3) we get

$x_5-\frac{7}{8}{x}_5=8$

$⟹\frac{8-7}{8}{x}_5=8$

$⟹x_5=64$

Therefore, the temperature on the fifth day is $64$ degrees.