5) Apti on mathematical ability ( Time & Work )

 1) A+B+C can do a work in 12 days. B+ C can do work in 18 days. A+ B can do work un 15 days. If b do the work alone, then how many days needed

We are given:

• A + B + C can do the work in 12 days

• B + C can do the work in 18 days

• A + B can do the work in 15 days

We are to find how many days B alone will take to complete the work.

We are given:

• A + B + C can do the work in 12 days

• B + C can do the work in 18 days

• A + B can do the work in 15 days

We are to find how many days B alone will take to complete the work.

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Step 1: Convert to Work Rates

Let the total work be LCM of 12, 18, 15 = 180 units (assume total work is 180 units for easier calculation).

Now compute each group’s work per day:

• (A + B + C)’s rate = 180 / 12 = 15 units/day

• (B + C)’s rate = 180 / 18 = 10 units/day

• (A + B)’s rate = 180 / 15 = 12 units/day

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Step 2: Subtract to find individual rates

From above:

• A + B + C = 15

• B + C = 10
  So, A = 15 − 10 = 5 units/day

Also:

• A + B = 12
  We already know A = 5, so:

• B = 12 − 5 = 7 units/day

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Step 3: Find Days for B to Finish Work Alone

If B works at 7 units/day, and total work is 180 units:

$$\text{Days} = \frac{180}{7} \approx 25.71 \text{ days}$$

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✅ Final Answer:

B alone will take approximately 25.71 days (or 25 days and 5 hours) to complete the work