Question

Give two real life problems applying the concept of arithmetic series and give the solution.​

Answer 1

Answer:

Let us write the penalty amount paid by the construction company from the first day as sequence

4000,5000,6000,..

The company can pay 165000 as penalty for this delay at maximum.

So, we have to write this amount as series

4000 + 5000 + 6000 +...

and the sum of the penalty amount is 165000.

Sn  =  165000

(n/2)[2a +(n - 1)d]  =  165000

Substitute a  =  4000 and d  =  1000.

(n/2)[2(4000) + (n  -1)1000]  =  165000

(n/2)[8000 + (n - 1)1000]  =  165000

(n/2)[8000 + 1000n - 1000]  =  165000

(n/2)[7000 + 1000n]  =  165000

n[7000 + 1000n]  =  165000 x 2

7000n + 1000n2  =  330000

Divide each side by 1000.  

7n + n2  =  330

n2 + 7n - 330  =  0

(n - 15)(n + 22)  =  0

n  =  15, -22

Here 'n' represents number of days delayed.

So it must be positive.

Therefore the correct answer is 15.

Answer 2

Step-by-step explanation:

Let total no. of people in the group be 100 and out of them x are men

Let total no. of people in the group be 100 and out of them x are meni.e no of women = 100−x.

Let total no. of people in the group be 100 and out of them x are meni.e no of women = 100−x.Mean age = no of peoplesum of ages in the group

Let total no. of people in the group be 100 and out of them x are meni.e no of women = 100−x.Mean age = no of peoplesum of ages in the groupTotal sum = sum of ages of men + sum of ages of women

Let total no. of people in the group be 100 and out of them x are meni.e no of women = 100−x.Mean age = no of peoplesum of ages in the groupTotal sum = sum of ages of men + sum of ages of women⇒100×25=x×26+(100−x)×21

Let total no. of people in the group be 100 and out of them x are meni.e no of women = 100−x.Mean age = no of peoplesum of ages in the groupTotal sum = sum of ages of men + sum of ages of women⇒100×25=x×26+(100−x)×21⇒x=80

Let total no. of people in the group be 100 and out of them x are meni.e no of women = 100−x.Mean age = no of peoplesum of ages in the groupTotal sum = sum of ages of men + sum of ages of women⇒100×25=x×26+(100−x)×21⇒x=80Hence, the percentage of men and women in the group is 80,20 respectively