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Solve the following question and mark the best possible option.
On a certain day, Vijay works at 11/8th of his usual rate of doing work and completes a work 33 minutes earlier than the usual time required. Had Vijay worked at 5/9th of his usual rate of doing work, then the time taken by him to complete the work would have been how much more than the usual  time required?
  • a)
    48.8 minutes   
  • b)
    96.8 minutes    
  • c)
    88 minutes    
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Solve the following question and mark the best possible option.On a ce...
Let the normal time taken by Vijay to complete the work be t.
As Vijay works at 11/8th of the normal rate, the time required will be 8/11th of the normal time i.e. (7/11)t
t – (8/11)t = 33 minutes ⇒ t = 121 minutes
When Vijay works at 5/9th of the normal rate, the Time required would be (9/5)th of the normal time i.e. 9/5 × 121 minutes = 217.8 minutes.
Thus Vijay required 217.8 – 121 = 96.8 more minutes to complete the work.
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Solve the following question and mark the best possible option.On a ce...
Question Analysis:
Let's assume the usual rate of work done by Vijay is "x" units per minute, and the usual time required by him to complete the work is "t" minutes.

According to the given information:
Vijay works at 11/8th of his usual rate of doing work, so his new rate of work is (11/8)x units per minute.
He completes the work 33 minutes earlier than the usual time required, so his new time taken is (t - 33) minutes.

We need to find the time taken by Vijay to complete the work if he had worked at 5/9th of his usual rate of doing work, and compare it with the usual time required.

Solution:
Step 1: Derive equations from the given information:
Using the formula: Rate × Time = Work, we can write the following equations:
Usual work done = Rate × Usual time = x × t
New work done = New rate × New time = (11/8)x × (t - 33)

Step 2: Simplify the equations:
Usual work done = x × t
New work done = (11/8)x × (t - 33)

Step 3: Calculate the time taken if Vijay had worked at 5/9th of his usual rate:
Let the new time taken be "t1" minutes.
Using the formula: New rate × New time = Usual work done, we can write the equation:
(5/9)x × t1 = x × t

Step 4: Simplify the equation:
(5/9)x × t1 = x × t
t1 = (9/5) × t

Step 5: Find the difference in time:
Difference in time = t1 - t = (9/5) × t - t = (4/5) × t

Step 6: Calculate the value of (4/5) × t:
Given that (4/5) × t = 33 minutes
t = (33 × 5)/4 = 165/4 = 41.25 minutes

Step 7: Convert the time to minutes and seconds:
41.25 minutes = 41 minutes and 0.25 × 60 = 15 seconds

Therefore, the time taken by Vijay to complete the work if he had worked at 5/9th of his usual rate would have been 41 minutes and 15 seconds more than the usual time required.

Step 8: Find the difference in minutes only:
41 minutes and 15 seconds = 41 minutes + 15/60 minutes = 41.25 minutes

Therefore, the time taken by Vijay to complete the work would have been 41.25 minutes more than the usual time required.

Step 9: Compare the options:
The options provided are:
a) 48.8 minutes
b) 96.8 minutes
c) 88 minutes
d) None of these

Comparing the calculated value of 41.25 minutes with the given options, we can see that the closest option is 96.8 minutes (option b).

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Solve the following question and mark the best possible option.On a certain day, Vijay works at 11/8th of his usual rate of doing work and completes a work 33 minutes earlier than the usual time required. Had Vijay worked at 5/9th of his usual rate of doing work, then the time taken by him to complete the work would have been how much more than the usual time required?a)48.8 minutes b)96.8 minutes c)88 minutes d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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