Ram is thrice efficient than Shyam and therefore able to finish the wo

1.	Ram is thrice efficient than Shyam and therefore able to finish the work in 15 days less than Shyam. In how many days they finish the work if they work together?1. 5.625 days2. 7.5 days3. 9.6 days4. 3.125 days
Answer» Correct Answer - Option 1 : 5.625 days Given: Ram is thrice efficient than Shyam and Ram finishes the work in 15 days less than Shyam Concept used: If time taken finish the work = X days ∴ Part of work completed in one day = 1/X Efficiency ∝ 1/Time Calculation: Ram is thrice efficient than Shyam ∴ Ratio of Efficiency = 3 ∶ 1 And ratio of the time taken = 1 ∶ 3 Now, Ram takes 15 days less than shyam to finish the work ∴ 3x – x = 15 ⇒ x = 7.5 So, Ram takes 7.5 days and Shyam takes 22.5 days to finish the work Now, Let both takes x days to finish the work ∴ Time taken by both to finish the work = (1/7.5 + 1/22.5) = 1/x ⇒ x = 5.625 days So, both of them will finish the work in 5.625 days Hence, option (1) is correct

Ram is thrice efficient than Shyam and therefore able to finish the work in 15 days less than Shyam. In how many days they finish the work if they work together?1. 5.625 days2. 7.5 days3. 9.6 days4. 3.125 days

Answer» Correct Answer - Option 1 : 5.625 days

Given:

Ram is thrice efficient than Shyam and Ram finishes the work in 15 days less than Shyam

Concept used:

If time taken finish the work = X days

∴ Part of work completed in one day = 1/X

Efficiency ∝ 1/Time

Calculation:

Ram is thrice efficient than Shyam

∴ Ratio of Efficiency = 3 ∶ 1

And ratio of the time taken = 1 ∶ 3

Now, Ram takes 15 days less than shyam to finish the work

∴ 3x – x = 15

⇒ x = 7.5

So, Ram takes 7.5 days and Shyam takes 22.5 days to finish the work

Now, Let both takes x days to finish the work

∴ Time taken by both to finish the work = (1/7.5 + 1/22.5) = 1/x

⇒ x = 5.625 days

So, both of them will finish the work in 5.625 days

Hence, option (1) is correct