Commercial Arithmetics : Pipes and Cistern

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Pipes and Cistern

what you'll learn...

overview

An example to the rate $\times$ $xx$ span $=$ $=$ aggregate, is
fill-rate $\times$ $xx$ time $=$ $=$ amount-filled.

This is explained in detail for pipes and cisterns.

examples in pipe-custern

A pipe fills a cistern in $12$ $12$ hours. The fill-rate of the pipe $= \frac{1}{12}$ $=1/12$ cistern per hour.

Unitary method in pipe-cistern:
The volume filled in $1$ $1$ unit time is the fill-rate.

A pipe fills a cistern in $12$ $12$ hours.
The fill-rate of the pipe is $\frac{1}{12}$ $1/12$ a cistern per hour.

A pipe fills at $\frac{1}{4}$ $1/4$ cistern an hour. How long does it take to complete filling $3$ $3$ cisterns?

Fill rate $= \frac{1}{4}$ $= 1/4$ of cistern
Volume filled $= 3$ $= 3$ cisterns
fill rate $\times$ $xx$ time $=$ $=$ volume filled
time $= 3 \div \frac{1}{4}$ $= 3 -: 1/4$ $= 12$ $=12$ hours

A pipe fills $3$ $3$ cisterns in $4$ $4$ hours. How many cisterns would be filled by the pipe in $12$ $12$ hours?

fill rate $\times$ $xx$ time $=$ $=$ volume filled

Fill rate and time are given. Volume filled is calculated.

The volume $= \frac{3}{4} \times 12 = 9$ $= 3/4 xx 12 = 9$ cisterns.

A pipe fills a cistern at $\frac{1}{12}$ $1/12$ cistern per hour and fills $3$ $3$ cisterns in a given time. If the fill-rate is increased to $\frac{1}{9}$ $1/9$ cistern per hour, how many cisterns would be filled in the same time?

fill rate $\times$ $xx$ time $=$ $=$ volume filled
fill rate and fill volume are in direct variation.

The number of cisterns $= 3 \div \frac{1}{12} \times \frac{1}{9} = 4$ $= 3 -: 1/12 xx 1/9 = 4$

A pipe takes $15$ $15$ hours to complete filling $3$ $3$ cisterns. If the number of cisterns is increased to $5$ $5$ , how much time does the pipe take to fill them?

fill rate $\times$ $xx$ time $=$ $=$ volume filled
time and fill volume are in direct variation.

The time $= \frac{15}{3} \times 5 = 25$ $= 15/3 xx 5 = 25$ hours.

A pipe fills at $\frac{1}{4}$ $1/4$ cistern per hour rate and take $8$ $8$ hours to complete filling a number of cisterns. If the fill rate is increased to $1$ $1$ cistern per hour, how much time does it take to fill the same number of cisterns?

fill rate $\times$ $xx$ time to fill $=$ $=$ volume filled
fill rate and time are in inverse variation.

The time = $\frac{1}{4} \times 8 \div 1 = 2$ $1/4 xx 8 -: 1 = 2$ hours

One pipe takes $20$ $20$ hours to fill $3$ $3$ cisterns and another pipe takes $15$ $15$ hours to fill $2$ $2$ cisterns. If these fill together, how much time do the pipes take to fill $17$ $17$ cisterns?

Fill rate of first pipe $= \frac{3}{20}$ $= 3/20$
fill rate of second pipe $= \frac{2}{15}$ $= 2/15$

Combined fill rate of the two pipes
$= \frac{3}{20} + \frac{2}{15}$ $= 3/20 + 2/15$
$= \frac{9 + 8}{60}$ $=(9+8)/60$
$= \frac{17}{60}$ $= 17/60$

fillrate $\times$ $xx$ time $=$ $=$ volume
$\frac{17}{60} \times$ $17/60 xx$ time = $17$ $17$
time $= 17 \div \frac{17}{60}$ $=17 -: 17/60$
$= 60$ $=60$ hours

summary

Problems in Pipe-Cistern : Simplify the problem to
fill rate $\times$ $xx$ time $=$ $=$ filled volume

There are three quantities in the equation. Possible formulation of questions are

• two quantities are given, and the third is asked.

• two quantities are given. If one of the given is modified, the changed second is asked. (direct or inverse variation)

Outline

The outline of material to learn "commercial arithmetics" is as follows.

Note: Click here for the detailed ouline of commercial arthmetics.

• Ratio, Proportion, Percentage

→ Comparing Quantities

→ Introduction to Ratio

→ Ration & Fraction Differences

→ ProportionsP

→ Percentages

→ Conversion to percentage

• Unitary Method

→ Introduction to Unitary Method

→ Direct Variation

→ Inverse Variation

→ DIV Pair

• Simple & Compound Interest

→ Story of Interest

→ Simple Interest

→ Compound Interest

• Rate•Span=Aggregate

→ Understanding Rate-Span

→ Speed • Time=Distance

→ Work-rate • time = Work-amount

→ Fill-rate • time = Filled-amount

• Profit-Loss-Discount-Tax

→ Profit-Loss

→ Discount

→ Tax

→ Formulas