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Let the rate at which one pipe fills the tank be RR (in tanks per hour).

Given that 6 pipes can fill the tank in 1 hour and 20 minutes, the total rate when using 6 pipes is 6R6R.

The time it takes to fill the tank (TT) is given by the formula:

T=Volume of the tankRate of fillingT=Rate of fillingVolume of the tank

Now, let's assume the volume of the tank is VV.

So, using 6 pipes: T1=V6RT1=6RV

Now, you want to find the time it takes when only 5 pipes are used. The rate with 5 pipes is 5R5R.

Using 5 pipes: T2=V5RT2=5RV

Now, we are given that T1=1T1=1 hour and 20 minutes. Convert this to minutes: T1=1 hour+20 minutes=60+20=80 minutesT1=1hour+20minutes=60+20=80minutes

Now, set up the equation using the given information: 80=V6R80=6RV

Solve for RR: R=V6×80R=6×80V

Now, substitute this value of RR into the equation for T2T2: T2=V5×V6×80T2=5×6×80VV

Simplify this expression to find T2T2, the time it takes when only 5 pipes are used.

Let's assume that the food provision is adequate for 100 students for 20 days.

The total person-days of food provision is given by multiplying the number of students by the number of days: 100 students×20 days=2000 person-days100students×20days=2000person-days.

Now, if 25 more students join, the total number of students becomes 100+25=125100+25=125. Let's find out how long the provisions will last for this increased number of students.

The total person-days for the new group is 125 students×days125students×days.

To find the number of days these provisions will last for the increased group, divide the total person-days by the number of students:

Calculate this expression to find the number of days the provisions will last for the increased group of 125 students.

The relationship between the number of workers, the time taken, and the amount of work done is given by the formula:

Work=Rate×TimeWork=Rate×Time

Let's assume that the amount of work required to build the wall is WW.

So, the rate of work for 15 workers is W4848W (work done per hour).

Now, if you want to find out how many workers are required to do the same amount of work in 30 hours, you can set up the equation:

W30=Rate×Number of workers30W=Rate×Number of workers

Given that the rate is W4848W for 15 workers:

W30=W48×Number of workers30W=48W×Number of workers

Now, solve for the number of workers:

Number of workers=W30W48Number of workers=48W30W

Number of workers=4830Number of workers=3048

Number of workers=85Number of workers=58

So, 8558 workers are required to do the same work in 30 hours. Since the number of workers cannot be in fractions, you might need to round up or down based on practical considerations. In this case, rounding up makes sense, so you would need 2 workers to complete the same work in 30 hours.

Let's calculate the effective cost per book after applying the 20% discount from the publisher.

The cost of each book from the local bookseller is Rs 90.

The discount offered by the publisher is 20%, which means she will pay only 80% of the original cost.

Effective cost per book from the publisher = 80% of Rs 90 Effective cost per book=0.8×90Effective cost per book=0.8×90

Now, let's find the number of books she can buy with the sanctioned amount.

Let NN be the number of books she can buy.

Total sanctioned amount = Total cost of books

N×Effective cost per book=Total sanctioned amountN×Effective cost per book=Total sanctioned amount

N×0.8×90=Total sanctioned amountN×0.8×90=Total sanctioned amount

Now, to find NN: N=Total sanctioned amount0.8×90N=0.8×90Total sanctioned amount

You need to know the total sanctioned amount to calculate the number of books she can buy. If you have that information, substitute it into the formula to find NN.

To calculate the cost of 15 pens when the cost of 20 pens is known, you can use the concept of proportion.

Let C20C20 be the cost of 20 pens, and C15C15 be the cost of 15 pens.

The relationship is proportional, so we can set up a proportion:

C2020=C=15C15

Given that C20=Rs.180C20=Rs.180, substitute this value into the proportion:

18020=C=15C15

Now, solve for C15C15:

C15=180×1520C15=20180×15

C15=270020C15=202700

C15=135C15=135

Therefore, the cost of 15 pens is Rs. 135.