Question

V. Answer the following 4 marks quesuns.
34) In the construction of building, building is not built in time charged fine Rs.50 per day. That as
1" day Rs. 200, 2nd day 250, 30 day 300 likely. A contractor takes 30 days late to complete the
building. Find the total amount of fine charges.

Answer 1

||✪✪ QUESTION ✪✪||

In the construction of building, building is not built in time charged fine Rs.50 per day. That as 1" day Rs. 200, 2nd day 250, 30 day 300 likely. A contractor takes 30 days late to complete the building. Find the total amount of fine charges.

|| ✰✰ ANSWER ✰✰ ||

Given That :-

→ 1St Day Fine = Rs.200

→ 2nd day Fine = Rs.250

→ 3rd day Fine = Rs.300.

So, on __________

As we can see, 200, 250, 300 ______________ Is a Series of AP.

Where ,

→ First Term = a = 200

→ Common Difference = 50

→ Number of Terms = n = 30 .

So,

→ Sum of n Terms of AP = (n/2)[2a + (n-1)d ]

Putting all value we get now,

→ Sn = (30/2)[2*200 + (30-1)*50 ]

→ Sn = 15 ( 400 + 29*50)

→ Sn = 15 (400 + 1450)

→ Sn = 15 * 1850

→ Sn = Rs.27750

Hence, the total amount of fine charges is Rs.27750.

Answer 2

Given :

• A fine of ₹ 50 was charged per day for delayed in construction of building.
• 1st day → ₹ 200 = a = $\sf{t_1}$
• 2nd day → ₹ 250 = $\sf{t_2}$
• 3rd day → ₹ 300 = $\sf{t_3}$
• It took 30 days to construct the building, n = 30

To Find :

• Total amount of fine charged, $\sf{S_n}$

Solution :

First term, a = 200

Second term = $\sf{t_2}$ = 250

Third term = $\sf{t_3}$ = 300

✪ Common difference, d :

• $\sf{t_2}$ - $\tt{t_1}$
• $\sf{250-200}$
• d = 50

Similarly, common difference among other terms too would be 50.

•°• The sequence forms an AP with common difference of 50.

✪ Since, we have to find the total fine, we will use the formula for sum of n terms of an AP.

Formula :

$\large{\boxed{\mathtt{\red{S_n\:=\:{\dfrac{1}{2}\:\times\:\big[2a\:+\:(n-1)\:d\big]}}}}}$

Block in the data,

$\mathtt{S_n\:=\:{\dfrac{30}{2}\:\times\:2(200)\:+\:(30-1)\:\times\:50}}$

➣ $\mathtt{S_n\:=\:15\:\times\:\:400\:+\:29\:\times\:50}$

➣ $\mathtt{S_n\:=\:15\:\times\:400\:+\:1450}$

➣ $\mathtt{S_n\:=\:15\:\times\:1850}$

➣ $\mathtt{S_n\:=\:27750}$

$\large{\boxed{\rm{\purple{Total\:Fine\:charged\:=\:Rs.\:27750}}}}$