Question

1. Mohit is building a wall with 650 bricks in it. On the first day, he manages to
lay 180 bircks. He gets more tired each day and lays 22 fewer bricks than
the day before. How many days will he take to build a wall?
[HOTS]​

Answer 1

21 1/2 days

650-180 = 470

470 divide by 22

To get 21.4 round off to get 21 and a half days

Answer 2

Answer:

The number of days taken by Mohit to complete the wall is found to be 5.

Step-by-step explanation:

The given situation is a case of Arithmetic progression series, in which there is a common difference.

The sum of the required terms of the series is 650. The first day, he lays off 180 bricks, making it the first term and with each day passing, he lays 22 less bricks, making -22 as the common difference.

Now, we have to find out the number of days required to build the wall, for that we know the expression of sum of 'n' terms of an Arithmetic progression is given by:

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

Now, substituting all values, we get:

$650=\frac{n}{2}(2(180)-22(n-1))$

Simplifying this, we get:

$1300=n(360-22n+22)$

$382n-22n^2-1300=0$

Now, solving the quadratic equation, we get:

$n=4.64\ or\ 12.71$

We will take the smaller solution and that too the nearest integer as the acceptable answer.

Thus, Mohit will take 5 days to build the wall completely.

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