Question

35) The average per day rainfall per a 15-day period at a hill
station was 125 mm per day. If every day from the second
day, there was an increase of 5 mm in, the rainfall over the
previous day, then what was the rainfall on the first day of
this period?
a) 95 mm
b) 110 mm
e) 90 mm
d) 105 mm​

Answer 1

The rainfall on the first day of this period = 90 mm

Given :

The average per day rainfall per a 15-day period at a hill station was 125 mm per day. If every day from the second day, there was an increase of 5 mm in, the rainfall over the previous day

To find :

The rainfall on the first day of this period is

a) 95 mm

b) 110 mm

c) 90 mm

d) 105 mm

Solution :

Step 1 of 4 :

Write down the given data

Here it is given that the average per day rainfall per a 15-day period at a hill station was 125 mm per day. If every day from the second day, there was an increase of 5 mm in the rainfall over the previous day

Since there was an increase of 5 mm in the rainfall over the previous day

So the rainfalls in 15-day period forms an arithmetic progression

Total rainfall in 15-day period

= 15 × 125 mm

Step 2 of 4 :

Find first term and common difference

We have to calculate the rainfall on the first day of this period

So first term = a = ?

Common Difference = d = 5

Step 3 of 4 :

Form the equation

We know that Sum of first n terms of an arithmetic progression

$= \displaystyle \sf \frac{n}{2} \bigg[2a + (n - 1)d \bigg]$

Where First term = a

Common Difference = d

Thus total rainfall in 15-day period

$= \displaystyle \sf \frac{n}{2} \bigg[2a + (n - 1)d \bigg]$

[ Putting n = 15 , d = 5 ]

$= \displaystyle \sf \frac{15}{2} \bigg[2a + (15 - 1) \times 5 \bigg]$

$= \displaystyle \sf \frac{15}{2} \bigg[2a + 70 \bigg]$

By the given condition

$\displaystyle \sf \frac{15}{2} \times \bigg[2a +70 \bigg] = 125 \times 15$

Step 4 of 4 :

Find rainfall on the first day of this period

$\displaystyle \sf \frac{15}{2} \times \bigg[2a +70 \bigg] = 125 \times 15$

$\displaystyle \sf{ \implies 2a + 70 =125 \times 2 }$

$\displaystyle \sf{ \implies 2a + 70 = 250 }$

$\displaystyle \sf{ \implies 2a = 250 - 70 }$

$\displaystyle \sf{ \implies 2a = 180}$

$\displaystyle \sf{ \implies a = 90}$

So the rainfall on the first day of this period = 90 mm

Hence the correct option is c) 90 mm

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