Problem Analysis:
Let's assume that the first pipe takes x minutes to fill the cistern, and the second pipe takes x + 3 minutes to fill the cistern. We need to find the time it takes for each pipe to fill the cistern when they work together.

Given Information:
- Two pipes can fill the cistern in 3 whole 1 upon 30 minutes when working together.
- One pipe takes 3 minutes more than the other to fill the cistern.

Solution:
To find the time it takes for each pipe to fill the cistern when they work together, we can use the concept of their work rates.

Let's assume the work rate of the first pipe is R1 (in units per minute) and the work rate of the second pipe is R2 (in units per minute).

Work Rate:
Work rate is the amount of work done per unit time. In this case, the work rate is the volume of the cistern filled per minute.

Calculating Work Rate:
Since the cistern can be filled by two pipes working together in 3 whole 1 upon 30 minutes, we can calculate the work rate of both pipes combined.

Work Rate of both pipes combined = 1 cistern / (3 whole 1 upon 30 minutes)

Converting 3 whole 1 upon 30 minutes to an improper fraction:
3 whole 1 upon 30 minutes = 3 + 1/30 = 3 + 1/30 = (3*30 + 1)/30 = 91/30

So, the work rate of both pipes combined is 1 cistern / (91/30 minutes) = 30/91 cisterns per minute.

Equating Work Rates:
The work rate of both pipes combined is equal to the sum of the individual work rates of the two pipes.

R1 + R2 = 30/91

Considering Individual Work Rates:
The work rate of each pipe can be calculated by taking the reciprocal of the time it takes for each pipe to fill the cistern.

R1 = 1/x
R2 = 1/(x + 3)

Equating Work Rates:
Substituting the individual work rates into the equation for the combined work rate:

1/x + 1/(x + 3) = 30/91

Common Denominator:
To simplify the equation, we can find the common denominator of x and x + 3, which is x(x + 3).

Multiplying both sides of the equation by x(x + 3):

(x + 3) + x = (30/91)(x)(x + 3)

Expanding and Simplifying:
2x + 3 = (30/91)(x^2 + 3x)

Multiplying both sides of the equation by 91 to eliminate the fraction:

182x + 273 = 30(x^2 + 3x)

Rearranging the Equation:
30x^2 + 90x - 182x - 273 = 0

30x^2 - 92x - 273 = 0

Solving the Quadratic Equation:

First of all it is 3whole 1/13.let the time taken by faster pipe to fill the cistern be X minutes.time taken=(x+3) minutesportion of the cistern filled by faster pipe in one minute= 1/xportion of the cistern filled by the slower pipe in one minute= 1/x+3portion of the cistern filled together by 2 pipes in one minute= 1÷40/13 =13/40according to question1/x + 1/x+3 = 13/40solving this we will get 13x^2 - 41x - 120 = 013x^2-65x+24x-120=0solve it yourselfx-5=0 either 13x+24=0hence X=5time taken by faster pipe=5minutesand by slower pipe= X+3=5+3=8minutes