Among four persons Anuj, Bhim, Carl and Dinesh. Anuj takes thrice as much time as Bhim to complete a piece of work. Bhim takes thrice as much time as Carl and Carl takes thrice as much time as Dinesh to complete the same work. If all together they take 3 days to complete the work. Find the time taken by Bhim alone to complete the work alone.a)20 daysb)30 daysc)40 daysd)50 dayse)None of theseCorrect answer is option 'C'. Can you explain this answer?

Question

Accepted Answer

Let Bhim takes x days alone to complete the job, so Anuj will take 3x days, Carl will take x/3 days and Dinesh will take x/9 days to complete the work alone
1/3x + 1/x + 3/x + 9/x = 1/3
Solve for x

Answer

A:B:C:D TIME RATIO 27:9:3:1
A:B:C:D WORK RATIO 1:3:9:27

So total work= 40 work/day
so total work in 3 days = 3*40 work (as it took 3 days to complete the task completely working all 4 people simultaneously)
so B will complete the task = total task / B's per day work
= 120/3=40 days.
Option C . DON'T MAKE IT HARD.
1/X + BLA BLA ARE NONSENSE ,THEY ALL TAKE SIGNIFICANT AMOUNT OF TIME.

Answer

Let's solve the problem step by step.

1. Assign variables:
- Let's assume that Dinesh takes x days to complete the work.
- Therefore, Carl will take 3x days, Bhim will take 9x days, and Anuj will take 27x days to complete the work.

2. Calculate the work done per day:
- If Dinesh takes x days to complete the work, then he completes 1/x of the work in one day.
- Similarly, Carl completes 1/(3x) of the work in one day, Bhim completes 1/(9x) of the work in one day, and Anuj completes 1/(27x) of the work in one day.

3. Calculate the total work done in 3 days:
- Since they all work together for 3 days, the total work done will be the sum of the work done by each person in 3 days.
- Total work done = (1/x + 1/(3x) + 1/(9x) + 1/(27x)) * 3

4. Simplify the expression:
- Total work done = (1/x) * (1 + 1/3 + 1/9 + 1/27) * 3
- Total work done = (1/x) * (40/27) * 3
- Total work done = (3/9) * (40/27) * 3
- Total work done = (40/27)

5. Set up the equation:
- The total work done is equal to 1 (since they complete the whole work), so we can set the equation:
- (40/27) = 1/x

6. Solve for x:
- Cross-multiply the equation:
- 40x = 27
- x = 27/40

7. Calculate the time taken by Bhim:
- Bhim takes 9x days to complete the work, so substituting the value of x:
- Bhim takes 9 * (27/40) days
- Bhim takes 243/40 days

Therefore, the time taken by Bhim alone to complete the work is 243/40 days, which is approximately 6.075 days.

Since none of the given options match the calculated value, the correct answer is e) None of these.

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