Write a program to calculate in how many days a work will be completed by three persons A, B and C together. A

Exercises · Q12

Q. Write a program to calculate in how many days a work will be completed by three persons A, B and C together. A, B, C take x days, y days and z days respectively to do the job alone. The formula to calculate the number of days if they work together is xyz/(xy + yz + xz) days where x, y, and z are given as input to the program.

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Concept understanding — Simple Interest Calculation

Simple Interest: The Cost of Borrowing (or the Reward for Saving)

Imagine you lend a friend ₹100. A year later, they return the ₹100. You're even — but you also missed the chance to use that ₹100 yourself for a whole year. That inconvenience has a price. In finance, that price is called interest.

Simple interest is the most straightforward way to calculate that price. It says: the interest you earn (or pay) each year is a fixed percentage of the original amount you started with — no matter how many years pass.

The Core Intuition

Think of it like renting money. If you rent a car for a day, you pay a fixed daily rate. If you rent it for 5 days, you pay 5 times that daily rate. Simple interest works the same way:

The Principal (P) is the amount you lend or borrow — the "car."
The Rate (R) is the daily rental charge, expressed as a percentage of the car's value — the "rent per day."
The Time (T) is how many days you keep the car — the number of years.

The total rent (interest) is just: daily rent × number of days.

The Precise Statement

\text{Simple Interest (SI)} = \frac{P \times R \times T}{100}

Where:

P = Principal (the original sum of money)
R = Rate of interest per year (in percent)
T = Time period (in years)

The Total Amount (A) you get back (or owe) at the end is:

A = P + \text{SI}

Why Divide by 100?

The rate $R$ is given as a percentage — say 10%. "10% per year" means you get ₹10 for every ₹100 you lend, each year. So for a principal $P$ , the interest for one year is:

\frac{10}{100} \times P = 0.10 \times P

That's the same as $\frac{P \times R}{100}$ . For $T$ years, you multiply by $T$ , giving $\frac{P \times R \times T}{100}$ .

A Worked Example

You deposit ₹2000 in a bank that offers 8% simple interest per year. You leave it for 3 years.

P = ₹2000
R = 8
T = 3

\text{SI} = \frac{2000 \times 8 \times 3}{100} = \frac{48000}{100} = ₹480

So after 3 years, you earn ₹480 in interest. Your total amount becomes:

A = 2000 + 480 = ₹2480

Tip

Notice that each year you earn exactly the same interest: $\frac{2000 \times 8}{100} = ₹160$ . Year 1: ₹160, Year 2: another ₹160, Year 3: another ₹160. The interest never grows because it's always calculated on the original ₹2000, not on the growing balance.

The Key Property (and its Limitation)

Simple interest is linear — the interest grows at a constant rate each year. This makes it easy to calculate and understand. …

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Translate the given formula days = xyz/(xy + yz + xz) directly:

x = float(input("Days taken by A alone: "))
y = float(input("Days taken by B alone: "))
z = float(input("Days taken by C alone: "))
days = (x * y * z) / (x*y + y*z + x*z)
print("Working together, the work is completed in", round(days, 2), "days")

Sample run (x = 6, y = 8, z = 12): xy + yz + xz = 48 + 96 + 72 = 216, xyz = 576, 576/216 ≈ 2.67: …

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Read x, y, z, apply days = xyz/(xy + yz + xz) and print — for the sample inputs 6, 8, 12 the three finish the work together in about 2.67 days.

The formula is supplied, so the whole task is a faithful translation into one arithmetic expression, with parentheses guaranteeing the entire denominator is computed before the division.

# Days to finish a work when A, B and C work together
x = float(input("Days taken by A alone: "))
y = float(input("Days taken by B alone: "))
z = float(input("Days taken by C alone: "))

days = (x * y * z) / (x*y + y*z + x*z)
print("Working together, the work is completed in", round(days, 2), "days")

Key lines:

The denominator must be parenthesised: x*y*z / x*y + y*z + x*z would divide only by x, then multiply by y — a completely different (and wrong) value. This is the pitfall the exercise is really about.
round(days, 2) keeps the report readable; drop it if full precision is wanted.

Sample run (an example — any positive inputs work):

Days taken by A alone: 6
Days taken by B alone: 8
Days taken by C alone: 12 …

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