Time and Work
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Q.

Ram starts working on a job and works on it for 12 days and completes $40%$ of the work. To help him complete the work, he employs Ravi and together they work for another 12 days and the work gets completed. How much more efficient is Ram than Ravi?

 A.

$50\%$

 B.

$200%$

 C.

$125\%$

 D.

$100%$

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Solution:
Option(D) is correct

Ram completes $40\%$ of work in 12 days i.e. another $60\%$ of the work has to be completed by Ram and Ravi.

They have taken 12 days to complete $60\%$ of the work.
Therefore, Ram and Ravi, working together, would have completed the entire work in \(\dfrac{12}{60}\times 100=20\) days

As Ram completes $40\%$ of the work in 12 days, he will take \(\dfrac{12}{40}\times 100=30\) days to complete the entire work

Working alone, we know Ram takes 30 days to complete the entire work.

Let us assume that Ravi takes '$x$' days to complete the entire work, if he works alone. And together, they complete the entire work in 20 days.

Therefore,

\(\dfrac{1}{30}+\dfrac{1}{x}=\dfrac{1}{20}\)

\(\dfrac{1}{x}=\dfrac{1}{20}-\dfrac{1}{30}=\dfrac{1}{60}\)

Therefore, Ravi will take 60 days to complete the work, if he works alone.

Hence, Ram is $100\%$ more efficient than Ram.


(2) Comment(s)


Poonam Pipaliya
 ()

Sir, how did you find percentage?

Please explain.

I don't get it..


Brenden
 ()

Since in the final answer $x=60$ days, so e, Ravi will take 60 days to complete the work, if he works alone.

Also, Ram takes $30$ days to complete the entire work. when he works alone. i.e. half of Ravi's time.

Thus, Ram is twice as efficient or $100%$ MORE efficient than Ravi.