Munna is twice efficient as Cheeku and Cheeku can do a piece of work in 40 days. Cheeku started the work and after a few days Munna joined him. They completed the work in 32 days. From the starting, for how many days they worked together?a)6 daysb)8 daysc)4 daysd)10 daysCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Understanding the Efficiency
Cheeku can complete the work in 40 days. Therefore, his work rate is:
- Work Rate of Cheeku = 1/40 (work per day)
Since Munna is twice as efficient as Cheeku, his work rate is:
- Work Rate of Munna = 2 * (1/40) = 1/20 (work per day)
Work Done by Cheeku and Munna
Let’s denote the number of days Cheeku worked alone as $ x $. After $ x $ days, Munna joined Cheeku, and they worked together for $ (32 - x) $ days to complete the work in a total of 32 days.
Calculating Total Work
The total work can be expressed in terms of Cheeku’s and Munna's contributions:
- Work done by Cheeku alone in $ x $ days: $ x \times (1/40) $
- Work done by both Cheeku and Munna in $ (32 - x) $ days:
- Combined rate = (1/40 + 1/20) = (1/40 + 2/40) = 3/40
- Work done = $ (32 - x) \times (3/40) $
The equation representing total work is:
$$ x \times (1/40) + (32 - x) \times (3/40) = 1 $$ (where 1 represents the complete work)
Simplifying the Equation
Multiplying through by 40 to eliminate the fraction:
$$ x + 3(32 - x) = 40 $$
Expanding and simplifying gives:
$$ x + 96 - 3x = 40 $$
$$ -2x + 96 = 40 $$
$$ -2x = 40 - 96 $$
$$ -2x = -56 $$
$$ x = 28 $$
Finding Days Worked Together
Now, substituting back:
- Days worked together = $ 32 - x $ = $ 32 - 28 = 4 $
Conclusion
Thus, Cheeku and Munna worked together for 4 days.
The correct answer is option C.

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