Question

what is the average rain of the week if the average rain of the first six days increased by 5mm due to 60 mm rain on the seven day ?​

Answer 1

Answer:

30mm

Step-by-step explanation:

Answer 2

The Average rain of the week is 30 mm .

Step-by-step explanation:

Given as :

The measurement of rain on seventh day = 60 mm

Let The average rain of the week = A

According to question

Average rain of six days = $\dfrac{x_1+x_2+x_3+x_4+x_5+x_6}{6}$

Average rain of seven days = $\dfrac{x_1+x_2+x_3+x_4+x_5+x_6+x_7}{7}$

Now, Since, Average rain of 6 days increase by 5 mm, when 60 mm rain on seventh days

i.e $\dfrac{x_1+x_2+x_3+x_4+x_5+x_6}{6}$  +  5  = $\dfrac{x_1+x_2+x_3+x_4+x_5+x_6+60}{7}$

Or, $\dfrac{x_1+x_2+x_3+x_4+x_5+x_6}{6}$  + 5 = $\dfrac{x_1+x_2+x_3+x_4+x_5+x_6}{7}$ + $\dfrac{60}{7}$

Or, $\dfrac{x_1+x_2+x_3+x_4+x_5+x_6}{6}$  - $\dfrac{x_1+x_2+x_3+x_4+x_5+x_6}{7}$ = $\dfrac{60}{7}$ - 5

Or, ( $x_1+x_2+x_3+x_4+x_5+x_6$ ) ( $\dfrac{1}{6}$ - $\dfrac{1}{7}$ ) = $\dfrac{60-35}{7}$

Or,  ( $x_1+x_2+x_3+x_4+x_5+x_6$ ) ( $\dfrac{7-6}{42}$ ) = $\dfrac{25}{7}$

Or,  ( $x_1+x_2+x_3+x_4+x_5+x_6$ ) ( $\dfrac{1}{42}$ )  =  $\dfrac{25}{7}$

Or, ( $x_1+x_2+x_3+x_4+x_5+x_6$ )  = $\dfrac{25}{7}$ × 42

i.e $x_1+x_2+x_3+x_4+x_5+x_6$  = 25 × 6

Or,, $x_1+x_2+x_3+x_4+x_5+x_6$ = 150                                          .............1

Again

∵   on seventh day , rain measure = $x_7$ = 60 mm                       ...........2

The average rain of the week = $\dfrac{x_1+x_2+x_3+x_4+x_5+x_6+x_7}{7}$  

i.e                                           A = $\dfrac{150+60}{7}$                     ( from 1 and 2 )

Or,                                          A = $\dfrac{210}{7}$

∴                                             A = 30 mm

So, The Average rain of the week = A = 30 mm

Hence,  The Average rain of the week is 30 mm . Answer