DS time and work

Jane can paint a wall in j hours and bill can paint a wall in b hours . They begin at noon together. If j and b are both even numbers is J = B ?
1. Jane and bill finish at 4:48 on
2. (J + B)^2 = 400

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1 Answer(s)

Hi Santosh,

Here the rate of work of Jane is 1/j

and rate of work of bill is 1/b

Both work together, 1/j + 1/b = j+b/jb

So both work together, time taken is jb/j+b .

Question : Is J = B ?

Given: J and B are both even numbers.

Lets for a moment assume J = B,

then from the above expression we get,

j^2 / 2j

Which is nothing but j/2, since j is even , j/2 has to be an integer.

So, if J = B, then time taken for both to work together has to be a integer.

Statement I is sufficient:

Because its given here, together they take 4 hours 48 mins, which is 24/5 hours thats not an integer.

So J cannot be equal to B. Our assumption is wrong.

Answer to the question is NO.

So sufficient.

Statement II is insufficient:

If J = 10 and B = 10, statement hold true. Answer to the question is YES.

But if J = 12 and B = 8, statement hold true. But answer to the question is NO.

Hope this helps.

Expert Answered on October 8, 2017.
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