Question

Anil and Bijal together can do a job in 4 days. If Anil can do job in 12 days , if he work alone, then how many days Bijal alone take to complete the job?

• A. 6 days
• B. 9 days
• C. 10 days
• D. 12 days

Hint:

To quickly solve simple time and work problems:
\[ \text{Bijal's Time} = \frac{\text{Product of Times}}{\text{Difference of Times}} = \frac{12 \times 4}{12 - 4} = \frac{48}{8} = 6\text{ days}. \]
This shortcut formula works for any two-person work rate problem.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Time and work problems are solved using the concept of work rates.
The work rate of an individual is the fraction of the total job they can complete in a single unit of time (such as one day).
When individuals work together, their individual work rates are added to find their combined work rate:
\[ \text{Rate}_{\text{together}} = \text{Rate}_A + \text{Rate}_B \] Key Formula or Approach:
Let the time taken by Anil alone to complete the job be $A$ days, and the time taken by Bijal alone be $B$ days.
If they can complete the job together in $T$ days, their relationship is expressed as: \[ \frac{1}{A} + \frac{1}{B} = \frac{1}{T} \]

Step 2: Detailed Explanation:
Let us identify the given values and solve for $B$:
- Combined time taken ($T$) $= 4\text{ days}$
- Combined work rate $= \frac{1}{4}$ of the job per day.
- Time taken by Anil alone ($A$) $= 12\text{ days}$
- Anil's work rate $= \frac{1}{12}$ of the job per day.
Substitute these rates into the work rate equation: \[ \frac{1}{12} + \frac{1}{B} = \frac{1}{4} \] Isolate the term $\frac{1}{B}$: \[ \frac{1}{B} = \frac{1}{4} - \frac{1}{12} \] Find a common denominator for the fractions on the right side (which is $12$): \[ \frac{1}{B} = \frac{3}{12} - \frac{1}{12} \] \[ \frac{1}{B} = \frac{2}{12} \] Simplify the fraction: \[ \frac{1}{B} = \frac{1}{6} \] Solve for $B$: \[ B = 6 \] Therefore, Bijal working alone will take $6\text{ days}$ to complete the entire job.

Step 3: Final Answer:
Bijal alone will take 6 days to complete the job.
Therefore, the correct option is (A).