Question

The average rainfall in a city for the first four days was recorded to be 0.40 inch. the rainfall on the last two days was in the ratio of 4 : 3. the average of six days was 0.50 inch. what was the rainfall on the fifth day?

Answer 1

Let the rainfall on each day be r(n) where n is no. of that day.

So, for 1st 4 days, we have

[ r(1) + r(2) + r(3) + r(4) ] / 4 = 0.40

r(1) + r(2) + r(3) + r(4) = 1.60....(i)

Average of 6 days =

[ r(1) + r(2) + r(3) + r(4) + r(5) + r(6) ] / 6 = 0.50

Putting (i) we get

1.60 + r(5) + r(6) = 3

r(5) + r(6) = 1.40

Rainfall on 5th and 6th day are in ratio 4:3

So, let r(5) = 4x and r(6) = 3x

4x + 3x = 1.40

7x = 1.40

x = 0.20

So, rainfall on 5th day is 0.2 x 4 = 0.80 inch

Answer 2

Hello Dear.

Let the amount of the rainfall in first four days be a,b,c and d inches.

Average Rainfall in four days = 0.40 inches.
∴ (a + b + c + d) ÷ 4 = 0.40
⇒ (a + b + c + d) = 0.40 × 4
∴ a + b + c + d = 1.6 inches.  ---------------eq(i)


Now, Let the rainfall in fifth and sixth (or last two) days be 4x and 3x respectively.

Also, According to the Question,

Average Rainfall of Six days = 0.50 inches.
∴ (a + b + c + d + 4x + 3x)/6 = 0.50
⇒ 1.6 + 7x = 0.50 × 6
⇒ 1.6 + 7x = 3
⇒ 3 - 1.6 = 7x
∴ 7x = 1.4
∴ x = 0.2 inches.


Rainfall in fifth days = 4x
= 4 × 0.2
= 0.8 inches.


Hence, the Rainfall in fifth day is 0.8 inches.


Hope it helps.