Question

A contractor agrees to dig a well 50 metres deep at a cost of Rs.1000 for the first metre, Rs.1040 for the second metre, Rs.1080 for the third metre and so on for the subsequent metres. The total cost to dig the well is

1. Rs.90,000
2. Rs.99,000
3. Rs.9000
4. Rs.1,00,000

Give me correct answer and explanation also and I wl mrk u as brainliest...​

Answer 1

Answer:

4. 1,00,000

Step-by-step explanation:

{(1000×50)} + {40(1275)}-1000

50000+51000-1000

1,00,000

Answer 2

Given:

A contractor agrees to dig a well 50 metres deep at a cost of Rs. 1000 for the first metre, Rs. 1040 for the second metre, Rs. 1080 for the third metre and so on for the subsequent metres. The total cost to dig the well is?

To find:

The total cost to dig the well is?

Solution:

The depth of the well agreed by the contractor to dig = 50 m

The cost of digging the well for the first metre = Rs. 1000

The cost of digging the well for the 2nd metre = Rs. 1040

The cost of digging the well for the 3rd metre = Rs. 1080

and so on . . .

From the above-given situation, we can clearly see that it resembles Arithmetic Progression where

n = no. of terms = 50

a₁ = first term = 1000

a₂ = second term = 1040

a₃ = third term = 1080

Common difference, d = 1040 - 1000 = 40 or 1080 -1040 = 40

To find the total cost to dig the well, we will calculate the sum of the cost of digging all 50 meters of the well i.e., the value of S₅₀.

We know,

$\boxed{\bold{S_n = \frac{n}{2} [2a + (n-1)d]}}$

Now, on substituting the value of n = 50, a = 1000 and d = 40 in the above formula, we get

$S_5_0 = \frac{50}{2} [(2\times 1000) + (50-1)40]}}$

$\implies S_5_0 = \frac{50}{2} [2000 + (49)40]}}$

$\implies S_5_0 = \frac{50}{2} [2000 + 1960]$

$\implies S_5_0 = \frac{50}{2} \times 3960$

$\implies S_5_0 = 25 \times 3960$

$\implies \bold{S_5_0 = 99,000}$ ← option (2)

Thus, the total cost of digging the well is → Rs. 99,000.

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Also View:

The cost of digging a well after every metre of digging when it costs 150 for the first meter and rises by rs 50 for the subsequent meter?

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