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Answer: After the withdrawal, Rajan's bank balance will be

6150 RS - 2050 RS = 4100 RS

Step-by-step explanation:

Initially, Rajan had 6000 RS in his bank account about a week ago. This indicates that the initial balance he possessed is 6000 RS.

One week later, he credited 150p RS to his account.

Thus, the current total in his account is

= 6000 RS + 150p RS = 6150 RS.

The following day, he withdrew one-third of his total balance. Therefore, the amount withdrawn is

1/3 × 6150 = 6150/3 = 2050 RS

After the withdrawal, his remaining balance in the bank will be the new total minus the amount withdrawn.

His remaining balance in the bank account post-withdrawal will be

6150 RS - 2050 RS = 4100 RS

Out of 100 surveyed individuals, 35 work out in the morning, 45 in the afternoon, and 20 at night.

Jim is accurate.....
The ratio of morning exercisers to the whole group is 35/100.
The ratio of afternoon exercisers is 45/100.
The ratio for night exercisers is 20/100.

A. The order in which you define the variables isn't fixed. For the sake of this discussion, let's define them like this:

x = Number of bookshelves
y = Number of tables

B. Due to the total number of items to produce, we have the following inequality based on those variables.

x + y > 25

Additionally, you can create a second inequality concerning your budget for materials.

20x + 45y < 675

Moreover, you should also add that both values must not be negative, since you can't produce negative tables.

C. By analyzing the constraints and solving the system, you will find that the feasible region contains 4 vertices.

(0,0)
(18, 7)
(0, 15)
(33.75, 0) or (33, 0) if you prefer to round it. 

Take note of the image below

the riverbank requires no fencing due to the river's presence
so the pen's perimeter can be calculated as 2w + l, or w + w + l
thus   

derive P(w), set it to zero, locate any critical points, and perform a first-derivative test for minimum values.

Dimensions of the rectangle are defined as Length=2x
Width=x
The formula for perimeter is given by 2(Length) + 2(Width).

First, we need to determine the dimensions of the rectangle, specifically its length and width.

We can derive this equation:
24=2(2x)+2(x)
4x+2x=24
6x=24
x=24/6
x=4

Consequently, Length becomes 2x, leading to 2(4)=8.

Therefore, the length is 8 inches and the width is 4 inches.

Next, we will calculate the area of the rectangle.
The area can be computed as Length multiplied by Width.

Area=(8 in)(4 in)=32 in²

Conclusion: The area of Marshall's rectangular poster is 32 in².