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Multiplication of Fractions

A and B can d...

Question

A and B can do a work alone exactly in $20$ and $25$ days respectively. However when they worked together they do $25 %$ more work than is expected . If they work for a few days alone and for few days together (both being integers only), then work could have been completed in exactly.

10

days

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14

days

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16

days

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17

days

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Solution

The correct options are
A $10$ days
C $16$ days
D $17$ days
Let the total work $= 100 %$
Efficiency of A $= \frac{100}{20} = 5 %$ per day
Efficiency of B $= \frac{100}{25} = 4 %$ per day
Efficiency of A and B combined $(A + B) = 9 % + 25 %$ of $9 = 11.25 %$ per day.
Now, $11.25 \times 8 = 90$ and $5 \times 2 = 10$ units
So, total days $= 10$ ...[ they together work for 8 days, A works for days more .
$11.25 \times 4 = 45$ and $5 \times 7 = 35$ , $4 \times 5 = 20$ .
Total days $= 16$
$11.25 \times 4 = 45$ and $4 \times 10 = 40$ , $5 \times 3 = 15$ .
Total days $= 17$

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A and B can do a work alone exactly in 20 and 25 days respectively. However when they worked together they do 25% more work than is expected . If they work for a few days alone and for few days together (both being integers only), then work could have been completed in exactly.

A and B can do a work alone exactly in $20$ and $25$ days respectively. However when they worked together they do $25 %$ more work than is expected . If they work for a few days alone and for few days together (both being integers only), then work could have been completed in exactly.