Rahul can do 1-2 of a piece of work in 6 days -while Rohit can do 1-4 of the same work in 2 days - in how many days can both do it together-

The correct option is A 6 We should use rate = worktime Rahul's rate =(1/2)6=112 Rohit's rate =(1/4)2=18 Now, combined rate of Rahul and Ro ...

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Byju's Answer

Standard VII

Mathematics

Simple Interest

Rahul can do ...

Question

Rahul can do $\frac{1}{2}$ of a piece of work in 6 days ,while Rohit can do $\frac{1}{4}$ of the same work in 2 days . in how many days can both do it together?

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Solution

The correct option is A $6$
We should use $r a t e = \frac{w o r k}{t i m e}$

Rahul's rate $= \frac{(\frac{1}{2})}{6} = \frac{1}{12}$

Rohit's rate $= \frac{(\frac{1}{4})}{2} = \frac{1}{8}$

Now, combined rate of Rahul and Rohit is $\frac{1}{12} + \frac{1}{8}$

$= \frac{2}{24} + \frac{3}{24} = \frac{5}{24}$

How many days does it take them, working together, to finish the job?
$W o r k = 1$
When work is $1$ , rate and time are inversely proportional (OR)
$t i m e = \frac{1}{r a t e}$

$t i m e = \frac{1}{(\frac{5}{24})}$

$t i m e = \frac{24}{5} = 4 \frac{4}{5} d a y s$

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